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1
Anigbogu, Winner, and Hamzeh Bardaweel. "A Metamaterial-Inspired Structure for Simultaneous Vibration Attenuation and Energy Harvesting." Shock and Vibration 2020 (June 13, 2020): 1–12. http://dx.doi.org/10.1155/2020/4063025.
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In this article, a magnetomechanical metamaterial structure capable of simultaneous vibration attenuation and energy harvesting is presented. The structure consists of periodically arranged local resonators combining cantilever beams and permanent magnet-coil systems. A prototype of the metamaterial dual-function structure is fabricated, and models are developed. Results show good agreement between model simulation and experiment. Two frequency bandgaps are measured: 205–257 Hz and 587–639 Hz. Within these bandgaps, vibrations are completely attenuated. The level of vibration attenuation in the first bandgap is substantially larger than the level of vibration attenuation observed in the second bandgap. Mode shapes suggest that bending deformations experienced by the local resonators in the second bandgap are less than the deformations experienced in the first bandgap, and most vibrational energy is localized within the first bandgap where the fundamental resonant frequency is located, i.e., 224 Hz. The ability of the fabricated metamaterial structure to harvest electric power in these bandgaps is examined. Results show that vibration attenuation and energy harvesting characteristics of the metamaterial structure are coupled. Stronger vibration attenuation within the first bandgap has led to enhanced energy harvesting capabilities within this bandgap. Power measurements at optimum load resistance of 15 Ω reveal that maximum power generated within the first bandgap reaches 5.2 µW at 245 Hz. Compared with state-of-the-art, the metamaterial structure presented here shows a significant improvement in electric power generation, at considerably lower load resistance, while maintaining the ability to attenuate undesired vibrations within the frequency bandgap.
2
Dong, Xingjian, Shuo Wang, Anshuai Wang, et al. "Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial." Applied Mathematics and Mechanics 45, no. 10 (2024): 1841–56. http://dx.doi.org/10.1007/s10483-024-3168-7.
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AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.
3
Yang, Fan, Zhaoyang Ma, and Xingming Guo. "Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression." Applied Mathematics and Mechanics 46, no. 1 (2025): 1–24. https://doi.org/10.1007/s10483-025-3204-7.
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AbstractA novel elastic metamaterial is proposed with the aim of achieving low-frequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.
4
Hajhosseini, Mohammad. "Analysis of complete vibration bandgaps in a new periodic lattice model using the differential quadrature method." Journal of Vibration and Control 26, no. 19-20 (2020): 1708–20. http://dx.doi.org/10.1177/1077546320902549.
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In this study, a new periodic lattice model with special vibration-absorbing properties is introduced. This periodic structure consists of the connected beam elements with circular cross-sections. Four models with different sets of cross-sectional radii are considered for this periodic lattice. The theoretical equations of longitudinal, torsional, and transverse vibrations of beams are solved using the combination of generalized differential quadrature and generalized differential quadrature rule methods to calculate the first three complete bandgaps. Investigating the effects of geometrical parameters on the bandgaps shows that all bands are close to each other for specific values of the cross-sectional radii. Having close bandgaps means that this periodic structure has a relatively wide bandgap in total. Furthermore, this wide band can move to low-frequency ranges by changing the lattice thickness. Absorbing both in-plane and out-of-plane vibrations over a wide bandgap at low-frequency ranges makes this periodic lattice a good vibration absorber. Verification of the analytical method using ANSYS software shows that the combination of generalized differential quadrature and generalized differential quadrature rule methods can be used for vibration analysis of two- or three-dimensional structures such as frames and trusses with high accuracy.
5
Guo, Peng, and Qizheng Zhou. "An Analytical, Numerical, and Experimental Investigation on Transverse Vibrations of a Finite Locally Resonant Beam." Shock and Vibration 2022 (June 13, 2022): 1–17. http://dx.doi.org/10.1155/2022/6875718.
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An analytical, numerical, and experimental investigation on the transverse vibrations of a finite beam with periodically arrayed beam-like resonators was carried out. A continuous-discrete model of the finite locally resonant beam was established by employing the “mass-spring- mass” subsystem. The analytical solution of the coupling vibration equations was derived based on the modal superposition method, and the analytical expression of average velocity response and vibration transmissibility were given. Then, the minimum periodic number of different units which could result in a bandgap was determined. Finally, the bandgap of a finite locally resonant beam was confirmed by a vibration experiment on a simply supported beam with twelve uniformly distributed beam-like resonators. The numerical and experimental results show that finite locally resonant beams have low-frequency bandgaps like infinite locally resonant beams, and the bandgap position is close to the resonance frequency of resonators. In addition, for a beam with a different type of locally resonant units, the minimum number of units that can generate the bandgap is nearly the same. Within considered frequency ranges, the experimental results are consistent with the theoretical results, meaning that the transverse vibration in locally resonant beams could be substantially attenuated. The conclusions may be supported to the application of locally resonant theory to control low-frequency vibration and radiation noise.
6
Muhammad, Shoaib, Shuai Wang, Fengming Li, and Chuanzeng Zhang. "Bandgap enhancement of periodic nonuniform metamaterial beams with inertial amplification mechanisms." Journal of Vibration and Control 26, no. 15-16 (2020): 1309–18. http://dx.doi.org/10.1177/1077546319895630.
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The aim of this study was to obtain bandgaps that are much better, that is at lower frequencies and in broader frequency ranges. Novel nonuniform metamaterial beams with periodically variable cross sections and inertial amplification mechanisms are designed and investigated by numerical and experimental methods. Flexural vibration equations of the nonuniform metamaterial beams are established, and the enhanced bandgap and vibration reduction properties are achieved by combining Bragg scattering and the inertial amplification mechanisms. Numerical results of the bandgaps for the periodic elastic beams with and without the inertial amplification mechanisms are validated by comparing them with the results of vibration experiments. Effects of the amplification mass and angle on the bandgap properties are investigated. Larger amplification mass and angle lead to much enhanced bandgap performances of the nonuniform metamaterial beams in lower to higher frequency ranges.
7
Wei, Wei, Feng Guan, and Xin Fang. "A low-frequency and broadband wave-insulating vibration isolator based on plate-shaped metastructures." Applied Mathematics and Mechanics 45, no. 7 (2024): 1171–88. http://dx.doi.org/10.1007/s10483-024-3160-6.
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AbstractA metamaterial vibration isolator, termed as wave-insulating isolator, is proposed, which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation. It consists of plate-shaped metacells, whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow. The bandgap mechanisms, vibration isolation properties, effects of key parameters, and robustness to complex conditions are clarified. As experimentally demonstrated, the wave-insulating isolator can improve the vibration insulation in the ranges of [50 Hz, 180 Hz] and [260 Hz, 400 Hz] by 15 dB and 25 dB, respectively, in contrast to the conventional isolator with the same first resonant frequency.
8
Guo, Zhiwei, Buliang Xie, Meiping Sheng, and Hao Zeng. "Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators." Applied Sciences 14, no. 4 (2024): 1467. http://dx.doi.org/10.3390/app14041467.
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In order to suppress the transverse vibration of a plate, a quasi-zero-stiffness (QZS) resonator with tunable ultralow frequency bandgaps was introduced and analyzed. The resonator was designed by introducing the quasi-zero-stiffness systems into mass-in-mass resonators. The plane wave expansion method was employed to derive the bandgap characteristics of the locally resonant (LR) plate with QZS resonators, and corresponding simulations were carried out by finite element method (FEM). The results show that an LR plate with a QZS resonator can provide two bandgaps, and the ranges of the bandgaps agree well with the vibration attenuation bands calculated by FEM. Owing to the introduction of the QZS system, the bandgaps can be easily transferred to a lower frequency or even an ultralow frequency. The damping of the QZS resonators can effectively broaden the vibration attenuation bands. In addition, the differentiated design of the bandgap frequencies can be realized to obtain broadband low-frequency transverse wave suppression performance. Finally, a mechanical structure design scheme was proposed in order to achieve flexible adjustment of the bandgap frequency, which significantly increases the engineering applicability of QZS resonators.
9
Yong, Jiawang, Wanting Li, Xiaojun Hu, Zhishuai Wan, Yiyao Dong, and Nenglian Feng. "Co-Design of Mechanical and Vibration Properties of a Star Polygon-Coupled Honeycomb Metamaterial." Applied Sciences 14, no. 3 (2024): 1028. http://dx.doi.org/10.3390/app14031028.
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Based on the concept of component assembly, a novel star polygon-coupled honeycomb metamaterial, which achieves a collaborative improvement in load-bearing capacity and vibration suppression performance, is proposed based on a common polygonal structure. The compression simulation and experiment results show that the load-bearing capacity of the proposed metamaterial is three times more than that of the initial metamaterial. Additionally, metal pins are attached and particle damping is applied to the metamaterial to regulate its bandgap properties; the influence of configuration parameters, including the size, number, position, and material of the metal pins, on bandgaps is also investigated. The results show that the bandgap of the proposed metamaterial can be conveniently and effectively regulated by adjusting the parameters and can effectively suppress vibrations in the corresponding frequency band. Particle damping can be used to continuously adjust the frequency of the bandgap and further enhance the vibration suppression capacity of the metamaterial in other frequency bands. This paper provides a reference for the design and optimization of metamaterials.
10
Han, Wenwen, and Shui Wan. "Flexural Wave Bandgaps in a Prestressed Multisupported Timoshenko Beam with Periodic Inerter-Based Dynamic Vibration Absorbers." Sustainability 15, no. 4 (2023): 3680. http://dx.doi.org/10.3390/su15043680.
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Locally resonant (LR) metamaterial structures possess bandgaps in which wave propagation is significantly attenuated. In this paper, we discuss flexural wave bandgaps in an LR beam subjected to a global axial force and multiple vertical elastic supports. An array of inerter-based dynamic vibration absorbers (IDVAs) was periodically attached to the LR beam. The flexural wave band structure of this prestressed multisupported LR beam was first derived using the transfer matrix method (TMM) and then explicitly illustrated through a numerical example. Four bandgaps were identified: a bandgap located in the low-frequency zone, a Bragg band generated by Bragg scattering, and two LR bands generated by the local resonance of the IDVAs. The effects of the IDVA parameters, axial force, and vertical elastic support on the properties of the bandgaps were evaluated. In particular, the bandgaps merged accompanied by an exchange of their edge frequencies. The bandwidth of the merged bandgap was nearly equal to the sum of the bandwidths of the bandgaps involved, indicating a method for controlling broadband flexural vibration through the bandgap splicing mechanism.
11
Xining, Zhao, Zhang Yongwang, Li Bo, Shen Chuangshi, Li Zewei, and Zhou Bo. "Active tuning of the vibration and wave propagation properties in electromechanical metamaterial beam." Journal of Applied Physics 132, no. 23 (2022): 234501. http://dx.doi.org/10.1063/5.0122301.
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Locally resonant metamaterial beams made from flexible substrates with piezoelectric layers can exhibit bandgap and vibration attenuation properties. However, the bandgap properties of the electromechanical metamaterials are limited by the electromechanical coupling coefficient. In order to effectively overcome this limitation of the locally resonant bandgaps, a locally resonant electromechanical metamaterial beam with piezoelectric actuators and sensors is presented, and the piezoelectric shunting technique and negative proportional feedback control strategy are combined. In this design, both negative capacitance ( NC) and inductance ( L) are incorporated into the shunt circuits. Then, the classical root locus method is employed to obtain single/multiple bandgaps and particular structural response by arranging the poles and zeros. Finally, the influences of the feedback control gain, the shunt circuit type, and the damping ratio on the bandgap properties and wave propagation behaviors are analyzed. Numerical results demonstrate that the single/multiple bandgaps can be obviously broadened by properly increasing the control gain. Specifically, adding negative capacitance in series to pure inductive circuit can generate wider absolute bandgaps at lower frequencies. The comparison of the frequency response and the bandgap characteristics reveals a very good agreement. Summarily speaking, combining the piezoelectric shunting technique and negative proportional feedback control strategy can effectively tune the vibration and wave propagation behavior.
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Lei, Xiaofei, Peng Chen, Heping Hou, Shanhui Liu, and Peng Liu. "Longitudinal vibration wave in the composite elastic metamaterials containing Bragg structure and local resonator." International Journal of Modern Physics B 34, no. 26 (2020): 2050232. http://dx.doi.org/10.1142/s021797922050232x.
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In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.
13
Qiang, Chenxu, Yuxin Hao, Wei Zhang, Jinqiang Li, Shaowu Yang, and Yuteng Cao. "Bandgaps and vibration isolation of local resonance sandwich-like plate with simply supported overhanging beam." Applied Mathematics and Mechanics 42, no. 11 (2021): 1555–70. http://dx.doi.org/10.1007/s10483-021-2790-7.
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AbstractThe concept of local resonance phononic crystals proposed in recent years provides a new chance for theoretical and technical breakthroughs in the structural vibration reduction. In this paper, a novel sandwich-like plate model with local resonator to acquire specific low-frequency bandgaps is proposed. The core layer of the present local resonator is composed by the simply supported overhanging beam, linear spring and mass block, and well connected with the upper and lower surface panels. The simply supported overhanging beam is free at right end, and an additional linear spring is added at the left end. The wave equation is established based on the Hamilton principle, and the bending wave bandgap is further obtained. The theoretical results are verified by the COMSOL finite element software. The bandgaps and vibration characteristics of the local resonance sandwich-like plate are studied in detail. The factors which could have effects on the bandgap characteristics, such as the structural damping, mass of vibrator, position of vibrator, bending stiffness of the beam, and the boundary conditions of the sandwich-like plates, are analyzed. The result shows that the stopband is determined by the natural frequency of the resonator, the mass ratio of the resonator, and the surface panel. It shows that the width of bandgap is greatly affected by the damping ratio of the resonator. Finally, it can also be found that the boundary conditions can affect the isolation efficiency.
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Zhang, Shengke, Denghui Qian, Zhiwen Zhang, and Haoran Ge. "Low-Frequency Bandgap Characterization of a Locally Resonant Pentagonal Phononic Crystal Beam Structure." Materials 17, no. 7 (2024): 1702. http://dx.doi.org/10.3390/ma17071702.
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This paper proposes a local resonance-type pentagonal phononic crystal beam structure for practical engineering applications to achieve better vibration and noise reduction. The energy band, transmission curve, and displacement field corresponding to the vibration modes of the structure are calculated based on the finite element method and Bloch-Floquet theorem. Furthermore, an analysis is conducted to understand the mechanism behind the generation of bandgaps. The numerical analysis indicates that the pentagonal unit oscillator creates a low-frequency bandgap between 60–70 Hz and 107–130 Hz. Additionally, the pentagonal phononic crystal double-layer beam structure exhibits excellent vibration damping, whereas the single-layer beam has poor vibration damping. The article comparatively analyzes the effects of different parameters on the bandgap range and transmission loss of a pentagonal phononic crystal beam. For instance, increasing the thickness of the lead layer leads to an increase in the width of the bandgap. Similarly, increasing the thickness of the rubber layer, intermediate plate, and total thickness of the phononic crystals results in a bandgap at lower frequencies. By adjusting the parameters, the beam can be optimized for practical engineering purposes.
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SUN, Xuyang, Zhong WANG, Jingjun ZHOU, Qian WANG, and Jingjian XU. "Study on vibration bandgap characteristics of a cantilever beam type local resonance unit." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 42, no. 4 (2024): 643–51. http://dx.doi.org/10.1051/jnwpu/20244240643.
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This article proposes a novel phononic crystal configuration consisting of a through-hole cantilever beam and a mass block, and conducts numerical analysis and experimental verification on the bandgap characteristics of a two-dimensional periodic array plate containing this configuration. The results indicate that there are multiple bending wave band gaps in the proposed structure, and the formation of the bandgap is due to the coupling between elastic waves in the matrix and the resonance characteristics of the local resonant structure. The width of the bandgap is related to the coupling strength. Further research has also found that the proportion of effective mass of the mode is a criterion for determining whether the mode generates a bandgap. At the same time, the regulation of band gaps by the cell constants and geometric parameters of local resonance units was studied. Based on the above research, by improving the original local resonance structure, more abundant bandgap features were obtained, providing a feasible approach for the design of broadband bandgaps. Finally, the vibration transmission rate of the finite period structural plate was obtained through simulation calculations and experiments, and its attenuation frequency band was basically consistent with the bandgap range, indicating that the structure has good low-frequency vibration reduction performance, which has broad engineering application prospects in the field of vibration and noise reduction.
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Yang, Fan, Zhaoyang Ma, and Xingming Guo. "Bandgap characteristics of the two-dimensional missing rib lattice structure." Applied Mathematics and Mechanics 43, no. 11 (2022): 1631–40. http://dx.doi.org/10.1007/s10483-022-2923-6.
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AbstractIn this paper, the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem. The tuning of the width and position of the bandgap is achieved by changing the local structural parameters, i.e., the rotation angle, the short beam length, and the beam thickness. In order to expand the regulation of the bandgap, the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed. The results show that the mass density and stiffness of the structure have significant effects on the bandgap, while Poisson’s ratio has no effect on the bandgap. By analyzing the first ten bands of the reference unit cell, it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction, and these bandgap widths are wider. The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure, and this dipole resonance originates from the coupling of the bending deformation of the beam elements. In the band structure, the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance, which is different from that with the conventional negative slope formed by the coupling of two resonance modes. This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials, as well as for the regulation of bandgaps and the suppression of elastic waves.
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Zhang, Zhen, Qin Wang, Yu Su, Junwei Tian, Xingang Wang, and Shoumin Wang. "The influence of component defect states on bandgaps of 2D composite beam frame structures." AIP Advances 13, no. 4 (2023): 045220. http://dx.doi.org/10.1063/5.0120259.
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This paper investigates the vibration bandgap properties of two-dimensional (2D) periodic composite beam frame structures with component defects. Combined with the topological characteristics of the structure, a generalized position coordinate system is proposed, and an assembly method of the stiffness matrix for the virtual full component model is presented. Then the spectral equations of motion of the whole 2D periodic composite beam frame structures and the ones with component defects are established. Compared with the frequency-domain solutions calculated using the finite element method, the accuracy and the feasibility of the spectral element method (SEM) solutions are verified. It can be shown that the SEM is suitable for analyzing the vibration bandgap properties, and the influence of different component defects and their combination on the bandgap characteristics of 2D periodic frame structures is studied. The results show that forbidden gap splitting will occur in the main bandgap of the structure, but the degree of influence varies. The results also show that the influence of component defects on unsymmetrical or irregular positions of the vibration bandgaps of periodic frame structures is greater than the one in symmetrical or regular positions.
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Liu, Jianing, Jinqiang Li, and Ying Wu. "Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method." Applied Mathematics and Mechanics 45, no. 10 (2024): 1807–20. http://dx.doi.org/10.1007/s10483-024-3167-8.
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AbstractSeveral types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps. In most of these structures, bandgaps are determined by their geometric configurations and material properties. This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate. The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results. In this method, the feedback voltage is related to the displacement of a resonator and the excitation frequency. By applying a feedback voltage on the piezoelectric fiber-reinforced composite (PFRC) layers attached to a cantilever-mass resonator, the natural frequency of the resonator can be adjusted. It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap. Based on this frequency-displacement feedback control strategy, the bandgap of the metamaterial plate can be effectively adjusted, and the vibration of the metamaterial plate can be significantly suppressed.
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Kao, De-Wei, Jung-San Chen, and Yu-Bin Chen. "Bandgap prediction for a beam containing membrane-arch-mass resonators." Journal of Applied Physics 132, no. 24 (2022): 244902. http://dx.doi.org/10.1063/5.0118530.
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This work aims to propose a promising locally resonating system consisting of a tensioned elastic membrane and two-arch masses attached on the membrane surface. Traditional membrane-type resonators, which usually create one obvious attenuation zone at low frequencies, might not be efficient in multi-frequency vibration suppression. The proposed structure can produce an extra clear flexural attenuation region and shift bandgap frequencies below 300 Hz. By adjusting geometric parameters (thickness, width, and location) of the arch mass, the bandgap region can be tuned. Introducing a feasible analytical model for accurately predicting the first and second initial frequencies of the bandgaps for a beam structure containing membrane-arch-mass resonators is another focus of this study. The proposed theoretical framework can be used to tune the bandgap to different target frequency ranges without knowing the actual width of the bandgap. Finite-element analysis and experiments are conducted to verify the theoretical predictions. A good agreement is seen among the theoretical, finite-element analysis, and experimental results. In addition, adjacent cells with different arch-mass distributions can generate two pairs of flexural bandgaps, increasing the practicality in engineering applications. The proposed structure might be used in low-frequency vibration isolation and filters.
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Annessi, A., V. Zega, P. Chiariotti, M. Martarelli, and P. Castellini. "An innovative wide and low-frequency bandgap metastructure for vibration isolation." Journal of Applied Physics 132, no. 8 (2022): 084903. http://dx.doi.org/10.1063/5.0102410.
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Engineering the architecture of materials is a new and very promising approach to obtain vibration isolation properties. The biggest challenge for lattice structures exhibiting vibration isolation properties is the trade-off between compactness and wide and low-frequency bandgaps, i.e., frequency ranges where the propagation of elastic or acoustic waves is prohibited. Here, we, both numerically and experimentally, propose and demonstrate a new design concept for compact metamaterials exhibiting extraordinary properties in terms of wide and low frequency bandgap and structural characteristics. With its 4 cm side length unit cell, its bandgap opening frequency of 1478 Hz, its band-stop filter behavior in the range 1.48–15.24 kHz, and its structural characteristics, the proposed [Formula: see text] metastructure represents great progress in the field of vibration isolation and a very promising solution for hand-held vibration probes applications that were unattainable so far through conventional materials.
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Tan, Xinyu, Bolong Jiang, Chunyu Qi, et al. "Method for Controlling Full-Frequency Band Environment Vibration by Coordinating Metro Vibration Sources and Propagation Paths." Applied Sciences 13, no. 24 (2023): 12979. http://dx.doi.org/10.3390/app132412979.
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Floating slab tracks (FSTs) are used to reduce the impact of vibration on precision instruments and historical relics along metro lines; however, ground vibration is universally amplified at the natural frequency of the tracks. In this study, a full-frequency control method that considers frequency matching for environmental vibrations, in combination with metro vibration sources and propagation paths, was developed based on the bandgap theory of the periodic structure. The effectiveness of this method was analysed by establishing a three-dimensional metro train–FST coupled model and a finite element analysis model of track bed–tunnel–soil–row piles. The results show that ground vibration can be reduced by approximately 3–5 dB at the natural frequency of the FST by adjusting the bandgap range of the periodic piles to 7–9 Hz, eliminating the adverse effect of vibration amplification at the natural frequency of the FSTs. The proposed control method shows good vibration control effects and can effectively minimise ground vibration in the full-frequency range.
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Gao, Weirui, Qian Zhang, Jie Sun, and Kai Guo. "A novel 3D-printed magnesium alloy phononic crystal with broadband bandgap." Journal of Applied Physics 133, no. 8 (2023): 085103. http://dx.doi.org/10.1063/5.0135770.
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This study proposes a novel approach to designing and fabricating a phononic crystal with embedded high-density resonators from 3D-printed magnesium alloy. The band structure and vibration suppression characteristics of the proposed structure are investigated using theoretical calculations and finite-element analysis. The bandgaps of the proposed phononic crystal are tuned using their superior structural design by changing the resonators. The effects of resonator mass on vibration suppression performance are also studied. The bandgap position and bandwidth are adjusted by changing the geometric parameters, broadening the application range. In addition, experiments are conducted to verify the bandgap accuracy. This study provides a new idea for constructing a 3D-printed magnesium alloy phononic crystal.
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Li, Chengfei, Zhaobo Chen, and Yinghou Jiao. "Vibration and Bandgap Behavior of Sandwich Pyramid Lattice Core Plate with Resonant Rings." Materials 16, no. 7 (2023): 2730. http://dx.doi.org/10.3390/ma16072730.
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The vibration suppression performance of the pyramid lattice core sandwich plates is receiving increasing attention and needs further investigation for technical upgrading of potential engineering applications. Inspired by the localized resonant mechanism of the acoustic metamaterials and considering the integrity of the lattice sandwich plate, we reshaped a sandwich pyramid lattice core with resonant rings (SPLCRR). Finite element (FE) models are built up for the calculations of the dispersion curves and vibration transmission. The validity of the bandgap of the SPLCRR and remarkable vibration suppression are verified by experimental observations and the numerical methods. Furthermore, the effects of geometric parameters, material parameters and period parameters on the bandgaps of the SPLCRR are systematically investigated, which offers a deeper understanding of the underlying mechanism of bandgap and helps the SPLCRR structure meet the technological update requirements of practical engineering design.
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Guo, Peng, Qi-zheng Zhou, and Zi-yin Luo. "Theoretical and experimental investigation on the low-frequency vibro-acoustic characteristics of a finite locally resonant plate." AIP Advances 12, no. 11 (2022): 115201. http://dx.doi.org/10.1063/5.0121331.
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This study investigates the low-frequency vibro-acoustic characteristics of a finite locally resonant (LR) plate. A dynamic model of the finite LR plate consisting of periodic arrays of beam-like resonators attached to a thin aluminum plate with simply supported boundary conditions is established, and the average vibration response and radiated efficiency are theoretically determined by using modal-superposition and harmonic-balance methods. In addition, the study investigates the influence of the parameters and number of additional resonators on the vibro-acoustic performance of the finite LR plate. Finally, a vibration experiment of a finite plate with 8 × 10 uniformly distributed beam-like resonators validates the theoretical analysis results. The numerical and experimental results show that the finite LR plate has a low-frequency bandgap that can suppress the vibration and radiated noise of the structure, and the bandgap position is close to the resonance frequency of resonators. The position and performance of bandgaps can be influenced by changing the parameters and number of resonators. The experimental results show a bandgap ranging from 370 to 425 Hz, which is consistent with the theoretical prediction. The finite LR plates proposed in this study can find potential applications in the attenuation of low-frequency vibration and noise.
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Li, Wenzhen, Quan Zhou, Zanxu Chen, Xi Ye, and Hongfu Wang. "Theoretical modeling and vibration characteristics analysis of acoustic black hole beam." Journal of Physics: Conference Series 2825, no. 1 (2024): 012032. http://dx.doi.org/10.1088/1742-6596/2825/1/012032.
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Abstract Acoustic Black Holes (ABH) can concentrate and capture the energy of waves in specific regions of a structure. They offer significant advantages and application potential in manipulating bending waves and reducing vibrations and noise in thin-walled structures. This paper focuses on the ABH beam structure, employing a semi-analytical method to analyze its vibration characteristics. Firstly, an improved triangular series is used as the displacement-permitting function for the ABH beam. Based on the Ritz method, a semi-analytical model for the ABH beam is established. The modal analysis of the ABH beam is solved, showing good agreement with numerical results, and validating the reliability of the semi-analytical method. Subsequently, the forced vibration response of the ABH beam is studied in comparison to a homogeneous beam. The bandgap characteristics and vibration-damping properties of the ABH beam are analyzed. The results indicate that the ABH beam has multiple vibration suppression bandgaps compared to a homogeneous beam, and after applying damping to the ABH beam, it exhibits a certain level of vibration suppression effect.
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Liu, Jiayang, and Shu Li. "A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties." Materials 16, no. 24 (2023): 7669. http://dx.doi.org/10.3390/ma16247669.
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The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study.
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Li, Shuqin, Jing Song, and Jingshun Ren. "Design of a Functionally Graded Material Phonon Crystal Plate and Its Application in a Bridge." Applied Sciences 13, no. 13 (2023): 7677. http://dx.doi.org/10.3390/app13137677.
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In order to alleviate the structural vibrations induced by traffic loads, in this paper, a phonon crystal plate with functionally graded materials is designed based on local resonance theory. The vibration damping performance of the phonon crystal plate is studied via finite element numerical simulation and the band gap is verified via vibration transmission response analysis. Finally, the engineering application mode is simulated to make it have practical engineering application value. The results show that the phonon crystal plate has two complete bandgaps within 0~150 Hz, the initial bandgap frequency is 0.00 Hz, the cut-off frequency is 128.32 Hz, and the internal ratio of 0~100 Hz is 94.13%, which can effectively reduce the structural vibration caused by traffic loads. Finally, stress analysis of the phonon crystal plate is carried out. The results show that phonon crystals of functionally graded materials can reduce stress concentration through adjusting the band gap. The phonon crystal plate designed in this paper can effectively suppress the structural vibration caused by traffic loads, provides a new method for the vibration reduction of traffic infrastructure, and can be applied to the vibration reduction of bridges and their auxiliary facilities.
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Anigbogu, Winner, and Hamzeh Bardaweel. "A Comparative Study and Analysis of Layered-Beam and Single-Beam Metamaterial Structures: Transmissibility Bandgap Development." Applied Sciences 12, no. 15 (2022): 7550. http://dx.doi.org/10.3390/app12157550.
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Recently, layered-beam metamaterial structures have been gaining popularity in a variety of engineering applications including energy harvesting and vibration isolation. While both single-beam metamaterial structures and layered-beam metamaterial structures are capable of generating bandgaps, it is important to understand the limitations of each type of metamaterial structure in order to make informed design decisions. In this article, a comparative study of bandgap development in single-beam metamaterial structures and layered-beam metamaterial structures is presented. The results show that for the single-beam metamaterial structure, with equally spaced local resonator designs, only one significant bandgap is developed at approximately 300–415 Hz. This bandgap occurs near the resonant frequency of the local resonators, i.e., 309 Hz. The results also show that when the spacing and the design of the local resonators are desired to remain fixed, layering the horizontal beams offers a significant pathway for both lowering the bandgap and developing additional bandgaps. The double-layered beam-type metamaterial structure studied in this work generates two bandgaps at approximately 238–275 Hz and 298–410 Hz. When the goal is to keep the number of local resonators per beam constant, increasing the length of the unit cells offers an alternative technique for lowering the bandgaps.
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Wu, Kun, Haiyan Hu, and Lifeng Wang. "Optimization of a type of elastic metamaterial for broadband wave suppression." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2251 (2021): 20210337. http://dx.doi.org/10.1098/rspa.2021.0337.
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The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.
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Guo, Zhiwei, and Meiping Sheng. "Bandgap of flexural wave in periodic bi-layer beam." Journal of Vibration and Control 24, no. 14 (2016): 2970–85. http://dx.doi.org/10.1177/1077546316640975.
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A periodic bi-layer beam structure is proposed and the bandgap characteristic of flexural wave is studied in this paper. The single cell is made up of two bi-layer beams with four components. For the infinite structure, the flexural wave bandgap frequency algorithm is theoretically derived through Timoshenko beam theory, Hamilton principle, Bloch-Floquet theory and transfer matrix method. An analytical example is presented to illustrate the bandgap characteristic and FEA software simulation is conducted to demonstrate the validation of the algorithm. For the finite structure, the vibration transmission characteristic is studied with FEA software to show the flexural wave attenuation behavior of the periodic bi-layer beam. The results reveal that, the flexural wave is attenuated gradually in the stopband along the direction of wave propagation, while in the passband, it will propagate without attenuation. Comparisons with periodic single layer beam are studied to verify the convenience and flexibility of bi-layer beam. Finally, parametric influences on bandgaps are discussed, which will help the designers to make a better design for vibration reduction.
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Zhao, Caiyou, Liuchong Wang, Dongya Liu, Xing Gao, Xi Sheng, and Wang Ping. "Vibration control mechanism of the metabarrier under train load via numerical simulation." Journal of Vibration and Control 25, no. 19-20 (2019): 2553–66. http://dx.doi.org/10.1177/1077546319866036.
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The problem of ambient vibration caused by rail transit continues to grow, and control effect requirements of different vibration reduction measures are always increasing. A new kind of vibration isolator used for floating slab tracks (FST) has been developed, called a metabarrier. Based on the bandgap properties of phononic crystals, it can realize a better vibration reduction capacity in certain frequency ranges with the same vertical stiffness as the original device. In order to study the vibration reduction characteristics of metabarriers under actual train loading action, two vibration isolators—a steel-spring vibration isolator and a metabarrier—were used to establish a train–FST–substrate dynamic coupling model. This study shows that the reduction capacity influenced by the phononic crystal bandgap is stable under different train speeds. In addition, under train load, the metabarrier can be used not only to isolate vibration by means of the bandgap, but also to absorb vibration dynamically, further expanding the vibration reduction frequency range. With optimized frequency range, metabarriers can reduce the acceleration vibration level by more than 9 dB over steel-spring vibration isolators.
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Alimohammadi, Hossein, Kristina Vassiljeva, S. Hassan HosseinNia, and Eduard Petlenkov. "Bandgap Dynamics in Locally Resonant Metastructures: A General Theory of Internal Resonator Coupling." Applied Sciences 14, no. 6 (2024): 2447. http://dx.doi.org/10.3390/app14062447.
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The dynamics of metastructures, incorporating both conventional and internally coupled resonators, are investigated to enhance vibration suppression capabilities through a novel mathematical framework. A close-form formulation and a transfer function methodology are introduced, integrating control system theory with metastructure analysis, offering new insights into the role of internal coupling. The findings reveal that precise internal coupling, when matched exactly to the stiffness of the resonator, enables the clear formation of secondary bandgaps, significantly influencing the vibration isolation efficacy of the metastructure. Although the study primarily focuses on theoretical and numerical analyses, the implications of adjusting mass distribution on resonators are also explored. This formulation methodology enables the adjustment of bandgap characteristics, underscoring the potential for adaptive control over bandgaps in metastructures. Such capabilities are crucial for tailoring the vibration isolation and energy harvesting functionalities in mechanically resonant systems, especially when applied to demanding heavy-duty applications.
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Akl, Wael, Hajid Alsupie, Sadok Sassi, and Amr M. Baz. "Vibration of Periodic Drill-Strings with Local Sources of Resonance." Vibration 4, no. 3 (2021): 586–601. http://dx.doi.org/10.3390/vibration4030034.
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A new class of drill-strings is proposed for attenuating undesirable vibrations to ensure effective operation. The drill-string is provided with passive periodic inserts, which are integrated with sources of local resonance (LR). The inserts make the drill-string act as a low frequency pass mechanical filter for the transmission of vibration along the drill-string. Proper design of the periodic inserts with sources of LR tend to shift these stop bands towards zones of lower frequencies to enable confining the dominant modes of vibration of the drill-string within these bands. In this manner, propagation of the vibration along the drill-string can be completely blocked. A finite element model (FEM) is developed using ANSYS to investigate the bandgap characteristics of the proposed drill-string with sources of LR. The developed FEM accounts for bending, torsional, and axial vibrations of the drill-string in order to demonstrate the effectiveness of the periodic inserts with LR in simultaneous control of these combined modes as compared to conventional solid periodic inserts, which are only limited to controlling bending vibrations. The effect of the design parameters of the periodic inserts with LR on the bandgap characteristics of the drill-string is investigated to establish guidelines of this class of drill-strings.
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He, Qiang, Jingkai Nie, Yu Han, Yi Tian, Chao Fan, and Guangxu Dong. "Investigation on Low Frequency Bandgap of Coupled Double Beam with Quasi-Zero Stiffness for Power Transformer Vibration Control." Shock and Vibration 2022 (December 31, 2022): 1–14. http://dx.doi.org/10.1155/2022/5029189.
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To suppress low frequency vibration and noise generated by power transformer in residential area and achieve environment protection standards, a double-beam metamaterial is proposed, which is fabricated through periodically coupling silicon steel sheet and aluminum beams with Belleville quasi-zero stiffness spring (BQZSS). The double-beam metamaterial can be assembled with iron core of transformers as a whole to obtain the design of a low-noise transformer. Performing static analysis, the mechanical model of BQZSS is established and the relationship between restoring force, stiffness, and displacement can be obtained. Then, the mechanical properties of BQZSS are verified with the finite element method. On this basis, the governing equations of the unit cell of the double-beam metamaterial are derived using Euler–Bernoulli beam theory. According to Bloch theorem and boundary conditions, the dispersion relation of the double-beam metamaterial is deduced, and behaviors of flexural wave propagation in beams are investigated. The effects of structure parameters on bandgaps and dispersion properties are studied, and the low frequency vibration bandgap mechanism is revealed. Finally, the frequency response function (FRF) of the double-beam metamaterial with a finite length is calculated in ANSYS to verify the bandgap characteristics given by a theoretical model. The results show that the double-beam metamaterial can yield multiple low frequency bandgaps at 100 Hz, 200 Hz, 300 Hz, and 500 Hz for suppression of flexural vibration components of transformers, which benefits from Bragg scattering (BS) and the blend of BS and LR mechanisms. The opening and closing of the low frequency bandgaps and the attenuation constants within bandgaps can be tuned by choosing parameters of beams. These findings suggest that the coupling between beams can lead to novel dispersion properties, which provides a new control approach for low frequency vibration and noise in power transformer.
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I, Boris, and Jaesun Lee. "Numerical and Experimental Study of Low-Frequency Membrane Damper for Tube Vibration Suppression." Actuators 13, no. 3 (2024): 106. http://dx.doi.org/10.3390/act13030106.
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In modern days, low-frequency vibration is still challenging to suppress due to its high vibrational energy. A typical suppression method is to increase the object’s mass to reduce the amplitude of the vibration, but such a way is unsuitable in many cases. Membrane dampers can potentially eliminate the limitation and offer lightweight and compact damper. The idea is to decrease the stiffness and add additional mass to increase the dissipation of the vibration energy. For that, the membrane and an extra mass made of silicone rubber were used for the damper. Finite element eigenfrequency simulation showed the transformation of each mode to the damper mode, where the tube displacement was zero. Also, it showed the bandgap between modes in the frequency range from 106 Hz to 158 Hz. The experimental verification of clamped from both ends of the tube showed the predicted bandgap and absence of the resonance peak of the bare tube. Overall, the membrane damper showed good efficiency in extremely low frequencies and seems promising for vibration suppression.
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Shu, Hai-Sheng, Xing-Guo Wang, Ru Liu, et al. "Bandgap analysis of cylindrical shells of generalized phononic crystals by transfer matrix method." International Journal of Modern Physics B 29, no. 24 (2015): 1550176. http://dx.doi.org/10.1142/s0217979215501763.
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Based on the concept of generalized phononic crystals (GPCs), a type of 1D cylindrical shell of generalized phononic crystals (CS-GPCs) where two kinds of homogeneous materials are arranged periodically along radial direction was proposed in this paper. On the basis of radial, torsional shear and axial shear vibrational equations of cylindrical shell, the total transfer matrix of mechanical state vector were set up respectively, and the bandgap phenomena of these three type waves were disclosed by using the method of transfer matrix eigenvalue of mechanical state vector instead of the previous localized factor analyses and Bloch theorem. The characteristics and forming mechanism of these bandgaps of CS-GPCs, together with the influences of several important structure and material parameters on them were investigated and discussed in detail. Our results showed that, similar to the plane wave bandgaps, 1D CS-GPCs can also possess radial, torsional shear and axial shear wave bandgaps within high frequency region that conforms to the Bragg scattering effect; moreover, the radial vibration of CS-GPCs can generate low frequency bandgap (the start frequency near 0 Hz), as a result of the double effects of wavefront expansion and Bragg scattering effect, wherein the wavefront effect can be the main factor and directly determine the existence of the low frequency bandgaps, while the Bragg scattering effect has obvious enhancement effect to the attenuation. Additionally, the geometrical and material parameters of units have significant influences on the wave bandgaps of CS-GPCs.
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Yong, Jiawang, Yiyao Dong, Zhishuai Wan, Wanting Li, and Yanyan Chen. "Collaborative Design of Static and Vibration Properties of a Novel Re-Entrant Honeycomb Metamaterial." Applied Sciences 14, no. 4 (2024): 1497. http://dx.doi.org/10.3390/app14041497.
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A novel re-entrant honeycomb metamaterial based on 3D-printing technology is proposed by introducing chiral structures into diamond honeycomb metamaterial (DHM), named chiral-diamond-combined honeycomb metamaterial (CDCHM), and has been further optimized using the assembly idea. Compared with the traditional DHM, the CDCHM has better performance in static and vibration isolation. The static and vibration properties of the DHM and CDCHM are investigated by experiments and simulations. The results show that the CDCHM has a higher load-carrying capacity than that of the DHM. In addition, the vibration isolation optimal design schemes of the DHM and CDCHM are examined by experiments and simulations. It is found that the vibration suppression of the CDCHM is also improved greatly. In particular, the optimization approach with metal pins and particle damping achieves a wider bandgap in the low-frequency region, which can strengthen the suppression of low-frequency vibrations. And the introduction of particle damping can not only design the frequency of the bandgap via the alteration of the dosage, but also enhance the damping of the main structure. This work presents a new design idea for metamaterials, which provides a reference for the collaborative design of the static and vibration properties of composite metamaterials.
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Han, Donghai, Qi Jia, Yuanyu Gao, et al. "Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes." Applied Mathematics and Mechanics 45, no. 10 (2024): 1821–40. http://dx.doi.org/10.1007/s10483-024-3166-8.
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AbstractTo solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes, a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed. First, an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes, and a novel periodic structure unit model is constructed for vibration reduction. Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure, the material parameters, structural parameters, and the arrangement interval of the periodic structure unit are optimized. The finite element method (FEM) is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure. Then, the wave/spectrum element method (WSEM) and experimental test are used to verify the calculated results above. Lastly, the vibration attenuation characteristics of the structure under different conditions, such as rubber material parameters, mass ring material, and fluid-structure coupling effect, are analyzed. The results show that the structure can produce a complete bandgap of 46 Hz–75 Hz in the low-frequency band below 100 Hz, which can effectively suppress the low broadband vibration of the fluid-conveying pipe. In addition, a high damping rubber material is used in the design of the periodic structure unit, which realizes the effective suppression of each formant peak of the pipe, and improves the vibration reduction effect of the fluid-conveying pipe. Meanwhile, the structure has the effect of suppressing both bending vibration and longitudinal vibration, and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe. The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.
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Gao, Xu, Jiyuan Wei, Jiajing Huo, Zhishuai Wan, and Ying Li. "The Vibration Isolation Design of a Re-Entrant Negative Poisson’s Ratio Metamaterial." Applied Sciences 13, no. 16 (2023): 9442. http://dx.doi.org/10.3390/app13169442.
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An improved re-entrant negative Poisson’s ratio metamaterial based on a combination of 3D printing and machining is proposed. The improved metamaterial exhibits a superior load-carrying and vibration isolation capacity compared to its traditional counterpart. The bandgap of the proposed metamaterial can be easily tailored through various assemblies. Additionally, particle damping is introduced to enhance the diversity of bandgap design, improve structural damping performance, and achieve better vibration isolation at low and medium frequencies. An experiment and simulation were conducted to assess the static and vibration performances of the metamaterial, and consistent results were obtained. The results indicate a 300% increase in the bearing capacity of the novel structure compared to traditional structural metamaterials. Furthermore, by increasing the density of metal assemblies, a vibration-suppressing bandgap with a lower frequency and wider bandwidth can be achieved. The introduction of particle damping significantly enhanced the vibration suppression capability of the metamaterial in the middle- and low-frequency range, effectively suppressing resonance peaks. This paper establishes a vibration design method for re-entrant metamaterials, which is experimentally validated and provides a foundation for the vibration suppression design of metamaterials.
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Jiang, Hui, Chunfeng Zhao, Yingjie Chen, and Jian Liu. "Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation." Buildings 14, no. 9 (2024): 2591. http://dx.doi.org/10.3390/buildings14092591.
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Rayleigh waves are vertically elliptical surface waves traveling along the ground surface, which have been demonstrated to pose potential damage to buildings. However, traditional seismic barriers have limitations of high-frequency narrow bandgap or larger volume, which have constraints on the application in practical infrastructures. Thus, a new type seismic metamaterial needs to be further investigated to generate wide low-frequency bandgaps. Firstly, a resonator with a three-vibrator is proposed to effectively attenuate the Rayleigh waves. The attenuation characteristics of the resonator are investigated through theoretical and finite element methods, respectively. The theoretical formulas of the three-vibrator resonator are established based on the local resonance and mass-spring theories, which can generate wide low-frequency bandgaps. Subsequently, the frequency bandgaps of the resonator are calculated by the finite element software COMSOL5.6 based on the theoretical model and Floquet–Bloch theory with a wide ultra-low-frequency bandgap in 4.68–22.01 Hz. Finally, the transmission spectrum and time history analysis are used to analyze the influences of soil and material damping on the attenuation effect of resonators. The results indicate that the resonator can generate wide low-frequency bandgaps from 4.68 Hz to 22.01 Hz and the 10-cycle resonators could effectively attenuate Raleigh waves. Furthermore, the soil damping can effectively attenuate seismic waves in a band from 1.96 Hz to 20 Hz, whereas the material of the resonator has little effect on the propagation of the seismic waves. These results show that this resonator can be used to mitigate Rayleigh waves and provide a reference for the design of surface waves barrier structures.
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Yu, Junmin, Jaesoon Jung, and Semyung Wang. "Derivation and Validation of Bandgap Equation Using Serpentine Resonator." Applied Sciences 12, no. 8 (2022): 3934. http://dx.doi.org/10.3390/app12083934.
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Bandgap refers to a frequency band where free waves do not propagate. One of the characteristics of a bandgap is its ability to block the propagation of bending waves in a specific frequency band with a periodic structure. Additionally, it has been reported in previous studies that the vibration-reduction performance of a bandgap is superior to that of other reduction methods. A bandgap can be generated in various frequency bands through a simple parameter change in the unit structure. However, the bandgap for a desired frequency band can be determined accurately only with intensive simulations. To overcome this limitation, we have mathematically derived the bandgap using a serpentine spring as a unit structure. The bandgap equation is derived from the general mass–spring system and the final bandgap is derived by substituting the system into the serpentine resonator. The error map for the major design parameter is confirmed by comparing the derived bandgap with the simulation result. In addition, the theoretical bandgap is compared to the experiment value and the vibration-reduction performance of the serpentine resonator is also confirmed. Based on the theoretical and experimental result, the proposed serpentine resonator verifies that the bandgap can be derived mathematically without numerical analysis. Therefore, serpentine resonator is expected to have various applications since it dramatically reduces the time and cost for forming the bandgap of the desired frequency band.
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Li, Yuanyuan, Jiancheng Liu, Zhaoyu Deng, et al. "Acoustic three-terminal controller with amplitude control for nonlinear seismic metamaterials." AIP Advances 12, no. 7 (2022): 075312. http://dx.doi.org/10.1063/5.0099843.
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To design and optimize seismic metamaterials, the impacts of nonlinearity in different locations of locally resonant acoustic metamaterials on the dispersions and the variation of amplitude-dependent bandgaps are investigated in this paper. The research used theoretical calculations, namely, Lindstedt–Poincaré perturbation method and prediction method, and combined finite-element simulation. Summarizing from our research, the lower bandgap is sensitive when exposed to amplitude stimulation, when there arise nonlinear characteristics between matrices; while nonlinearity appears within the interior oscillator, amplitudes obtain a more intense influence on the bandgap, introducing an enormous magnitude of deviation between the upper bandgap and the lower bandgap. Based on the peculiar frequency-shift characteristics, an acoustic three-terminal controller is proposed as a conventional subsize acoustical device and nonlinear seismic metamaterials component. This controller enables the realization of modulating the value of output signals by adjusting the quantitative loading on the control port, without changing the input signals and the parameters of the apparatus validated with the finite-element simulation. The work may offer potential applications in low-frequency vibration reduction and external-controllable multi-functional acoustical devices.
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Gao, Ming, Zhiqiang Wu, and Zhijie Wen. "Effective Negative Mass Nonlinear Acoustic Metamaterial with Pure Cubic Oscillator." Advances in Civil Engineering 2018 (September 30, 2018): 1–15. http://dx.doi.org/10.1155/2018/3081783.
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Acoustic metamaterial, which can prohibit effectively the elastic wave propagation in the bandgap frequency range, has broad application prospects in the vibration and noise reduction areas. The Lindstedt–Poincaré method was utilized to analyze the dispersion curves of nonlinear metamaterial with a pure Duffing oscillator. The first-order perturbation solutions of acoustic and optical branches were obtained. Both the starting and cutoff frequencies of the bandgap are determined consequently. It was found that the soft/hard characteristics of pure Duffing oscillators could lead to the lower/upper movement of the starting and cutoff frequencies of the bandgap. By further researching the degraded linear system, the conclusion that actual nonlinear metamaterial bandgap region is wider than effective negative mass region is drawn and that both mass and stiffness ratio effect on the starting frequency is obtained. Effective positive mass can also lead to the vibration attenuation in bandgap. For nonlinear metamaterial, the translation effect of the external excitation amplitude on the bandgap range and the zero mass at the nonlinear bandgap cutoff frequency were discussed, and all above conclusion are identified by numerical analysis.
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Wei, Wenming, Dimitrios Chronopoulos, and Han Meng. "Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators." Materials 14, no. 17 (2021): 4759. http://dx.doi.org/10.3390/ma14174759.
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This paper investigates the influences of nonperiodic rainbow resonators on the vibration attenuation of two-dimensional metamaterial plates. Rainbow metamaterial plates composed of thin host plates and nonperiodic stepped resonators are considered and compared with periodic metamaterial plates. The metamaterial plates are modelled with the finite element modelling method and verified by the plane wave expansion method. It was found that the rainbow metamaterial plates with spatially varying resonators possess broader vibration attenuation bands than the periodic metamaterial plate with the same host plates and total mass. The extension of attenuation bands was found not to be attributed to the extended bandgaps for the two-dimensional metamaterial plates, as is generally believed for a one-dimensional metamaterial beam. The complete local resonance bandgap of the metamaterial plates is separated to discrete bandgaps by the modes of nonperiodic resonators. Although the additional modes stop the formation of integrated bandgaps, the vibration of the plate is much smaller than that of resonators at these modal frequencies, the rainbow metamaterial plates could have a distinct vibration attenuation at these modal frequencies and achieve broader integrated attenuation bands as a result. The present paper could offer a new idea for the development of plate structures with broadband vibration attenuation by introducing non-periodicity.
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Guo, Jin, Rui Zhao, and Yunbo Shi. "Towards Broadband High-Frequency Vibration Attenuation Using Notched Cross-Shaped Metamaterial." Micromachines 14, no. 2 (2023): 414. http://dx.doi.org/10.3390/mi14020414.
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This paper reports a plate-type metamaterial designed by arranging unit cells with variable notched cross-sections in a periodical array for broadband high-frequency vibration attenuation in the range of 20 kHz~100 kHz. The dispersion relation and displacement field of the unit cell were calculated by simulation analysis, and the causes of the bandgap were analyzed. By studying the influence of critical structural parameters on the energy band structure, the corresponding structural parameters of a relatively wide bandgap were obtained. Finally, the plate-type metamaterial was designed by arranging unit cells with variable notched cross-sections in the periodical array, and the simulation results show that the vibration attenuation amplitude of the metamaterial can reach 99% in the frequency range of 20 kHz~100 kHz. After fabricating the designed plate-type metamaterial by 3D printing techniques, the characterization of plate-type metamaterial was investigated and the experiment results indicated that an 80% amplitude attenuation can be obtained for the suppression of vibration with the frequency of 20 kHz~100 kHz. The experimental results demonstrate that the periodic arrangement of multi-size cell structures can effectively widen the bandgap and have a vibration attenuation effect in the bandgap range, and the proposed plate-type metamaterial is promising for the vibration attenuation of highly precise equipment.
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Li, Yinggang, Qingwen Zhou, Ling Zhu, and Kailing Guo. "Hybrid radial plate-type elastic metamaterials for lowering and widening acoustic bandgaps." International Journal of Modern Physics B 32, no. 26 (2018): 1850286. http://dx.doi.org/10.1142/s0217979218502867.
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In this paper, we present theoretical investigation on the wave propagation and acoustic bandgap characteristics in hybrid radial plate-type elastic metamaterials constituted of periodic double-sides composite stubs deposited on one-dimensional binary radial phononic crystal plate. The dispersion relations and the displacement fields of the eigenmodes are calculated by using the finite element method on the basis of two-dimensional axial symmetry models. Numerical results show that the proposed hybrid radial plate-type elastic metamaterial can generate lowering and widening acoustic bandgaps and yield a significant expansion of the relative bandwidth by a factor of 5 compared to the traditional radial plate-type elastic metamaterial with double-sided composite stubs. The displacement fields of the eigenmodes are applied to reveal the formation mechanism of lowering and widening acoustic bandgaps. In addition, the influences of the physical and geometrical parameters on the bandgaps are further performed. These low-frequency broadband acoustic bandgap properties in the radial plate-type elastic metamaterials can probably be applied to vibration and noise reduction in the rotary machines and structures.
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Qin, Qi, and Mei-Ping Sheng. "Analyses of multi-bandgap property of a locally resonant plate composed of periodic resonant subsystems." International Journal of Modern Physics B 32, no. 24 (2018): 1850269. http://dx.doi.org/10.1142/s0217979218502697.
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A locally resonant (LR) plate made up of a thin plate attached with different types of resonators is analyzed in this paper. Each periodic element may consist of one or more spring-mass resonators attached onto one and the same surface of the plate lattice. The correctness of theoretical plane wave expansion (PWE) method adopted in this paper is validated through the comparisons with the classical theory and finite element method (FEM). When composing the LR plate system with two types of periodic resonant subsystems, there will appear two complete bandgaps, while other additional resonators may cause mainly directional gaps, calculated theoretically and numerically. From the comparisons of band-structure curves between a two-resonator-per-unit-element (TR-UE) system and both corresponding one-resonator-per-unit-element (OR-UE) systems, the bandgap width of the TR-UE system are not stacking effects of two OR-UE systems due to resonance interaction of different types of resonators. Moreover, via the deformation contours by FEM, the correspondence between the vibration modes of subsystems and the bandgap frequencies is demonstrated. The finite plate with limited resonators of two periodic types of parameters is modeled to show visually how flexural waves propagate within/without the bandgaps. Further, by adjusting the damping characteristic of both types of resonators, vibration attenuation band can be broadened widely.
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Liu, Guoqing, and Denghui Qian. "Investigation of Bandgap Properties of a Piezoelectric Phononic Crystal Plate Based on the PDE Module in COMSOL." Materials 17, no. 10 (2024): 2329. http://dx.doi.org/10.3390/ma17102329.
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Aiming to address the vibration noise problems on ships, we constructed a piezoelectric phononic crystal (PC) plate structure model, solved the governing equations of the structure using the partial differential equations module (PDE) in the finite element softwareCOMSOL6.1, and obtained the corresponding energy band structure, transmission curves, and vibration modal diagrams. The application of this method to probe the structural properties of two-dimensional piezoelectric PCs is described in detail. The calculation results obtained using this method were compared with the structures obtained using the traditional plane wave expansion method (PWE) and the finite element method (FE). The results were found to be in perfect agreement, which verified the feasibility of this method. To safely and effectively adjust the bandgap within a reasonable voltage range, this paper explored the order of magnitude of the plate thickness, the influence of the voltage on the bandgap, and the dependence between them. It was found that the smaller the order of magnitude of the plate thickness, the smaller the order of magnitude of the band in which the bandgap was located. The magnitude of the driving voltage that made the bandgap change became smaller accordingly. The new idea of attaching the PC plate to the conventional plate structure to achieve a vibration damping effect is also briefly introduced. Finally, the effects of lattice constant, plate width, and thickness on the bandgap were investigated.
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Xu, Lanhe, Xuche Cao, Xinbo Cui, and Bing Li. "Vibration Attenuation Performance of Meta-lattice Sandwich Structures with Truss-cores." Journal of Physics: Conference Series 2252, no. 1 (2022): 012030. http://dx.doi.org/10.1088/1742-6596/2252/1/012030.
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Abstract In recent years, lattice sandwich structures with truss-cores have shown great potential in lightweight, high load-bearing and multifunctional applications. However, there is still a lack of research on the vibration attenaution characteristics of such structures. In this paper, combined with the design concept of elastic metamaterial with the lattice truss-core sandwich structures, a meta-lattice sandwich structure with double-layer pyramidal truss core is proposed to realize superior vibration attenuation performance. Theoretical and numerical investigations are conducted on the bandgap mechanisms of the proposed meta-lattice structures. The efficient vibration suppression within the bandgap range is verified by numerical simulations. The results of this paper are of reference value for the design and engineering application of the lattice truss structure for vibration attenuation.
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Xu, Lanhe, Xuche Cao, Xinbo Cui, and Bing Li. "Vibration Attenuation Performance of Meta-lattice Sandwich Structures with Truss-cores." Journal of Physics: Conference Series 2252, no. 1 (2022): 012030. http://dx.doi.org/10.1088/1742-6596/2252/1/012030.
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Abstract In recent years, lattice sandwich structures with truss-cores have shown great potential in lightweight, high load-bearing and multifunctional applications. However, there is still a lack of research on the vibration attenaution characteristics of such structures. In this paper, combined with the design concept of elastic metamaterial with the lattice truss-core sandwich structures, a meta-lattice sandwich structure with double-layer pyramidal truss core is proposed to realize superior vibration attenuation performance. Theoretical and numerical investigations are conducted on the bandgap mechanisms of the proposed meta-lattice structures. The efficient vibration suppression within the bandgap range is verified by numerical simulations. The results of this paper are of reference value for the design and engineering application of the lattice truss structure for vibration attenuation.