Journal articles: 'Frequency response diagram'

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Mugarra, Asier, Hernan Mayora, Jose Manuel Guerrero, and Carlos A. Platero. "Frequency Response Analysis (FRA) Fault Diagram Assessment Method." IEEE Transactions on Industry Applications 58, no. 1 (January 2022): 336–44. http://dx.doi.org/10.1109/tia.2021.3131425.

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Vodopyanov, M. A., K. A. Menzorov, V. V. Davydov, and V. Yu Rud. "Method for reducing phase fluctuations of a precision frequency response meter for microwave quantum generators." Journal of Physics: Conference Series 2086, no. 1 (December 1, 2021): 012071. http://dx.doi.org/10.1088/1742-6596/2086/1/012071.

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Abstract The principle of operation of the device for measuring frequency characteristics is considered. Block diagram of a device for measuring the frequency characteristics of a digital frequency comparator with correlation quadrature processing and description of their components is illustrated. The block diagram of the frequency multiplier is given. The accuracy characteristics of the developed meter design are evaluated. They are compared with the characteristics of previously used devices. The Improve accuracy characteristics and increased stability of operation were found.

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Graetzel, Chauncey F., Bradley J. Nelson, and Steven N. Fry. "Frequency response of lift control in Drosophila." Journal of The Royal Society Interface 7, no. 52 (May 12, 2010): 1603–16. http://dx.doi.org/10.1098/rsif.2010.0040.

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The flight control responses of the fruitfly represent a powerful model system to explore neuromotor control mechanisms, whose system level control properties can be suitably characterized with a frequency response analysis. We characterized the lift response dynamics of tethered flying Drosophila in presence of vertically oscillating visual patterns, whose oscillation frequency we varied between 0.1 and 13 Hz. We justified these measurements by showing that the amplitude gain and phase response is invariant to the pattern oscillation amplitude and spatial frequency within a broad dynamic range. We also showed that lift responses are largely linear and time invariant (LTI), a necessary condition for a meaningful analysis of frequency responses and a remarkable characteristic given its nonlinear constituents. The flies responded to increasing oscillation frequencies with a roughly linear decrease in response gain, which dropped to background noise levels at about 6 Hz. The phase lag decreased linearly, consistent with a constant reaction delay of 75 ms. Next, we estimated the free-flight response of the fly to generate a Bode diagram of the lift response. The limitation of lift control to frequencies below 6 Hz is explained with inertial body damping, which becomes dominant at higher frequencies. Our work provides the detailed background and techniques that allow optomotor lift responses of Drosophila to be measured with comparatively simple, affordable and commercially available techniques. The identification of an LTI, pattern velocity dependent, lift control strategy is relevant to the underlying motion computation mechanisms and serves a broader understanding of insects' flight control strategies. The relevance and potential pitfalls of applying system identification techniques in tethered preparations is discussed.

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Lee, Pedro J., John P. Vítkovský, Martin F. Lambert, Angus R. Simpson, and James A. Liggett. "Discrete Blockage Detection in Pipelines Using the Frequency Response Diagram: Numerical Study." Journal of Hydraulic Engineering 134, no. 5 (May 2008): 658–63. http://dx.doi.org/10.1061/(asce)0733-9429(2008)134:5(658).

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BILLINGS, S. A., and O. M. BOAGHE. "THE RESPONSE SPECTRUM MAP, A FREQUENCY DOMAIN EQUIVALENT TO THE BIFURCATION DIAGRAM." International Journal of Bifurcation and Chaos 11, no. 07 (July 2001): 1961–75. http://dx.doi.org/10.1142/s0218127401003164.

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The Response Spectrum Map (RSM) is introduced as a frequency domain equivalent to the Bifurcation Diagram. The RSM is a map of the energy distribution of a system in the frequency domain, where subharmonics, superharmonics and chaos generation can be revealed. The RSM is used in this paper to qualitatively analyze and detect various dynamical states exhibited by a nonlinear system.

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Zhou, Shengxi, Junyi Cao, Grzegorz Litak, and Jing Lin. "Numerical analysis and experimental verification of broadband tristable energy harvesters." tm - Technisches Messen 85, no. 9 (September 25, 2018): 521–32. http://dx.doi.org/10.1515/teme-2017-0076.

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Abstract This paper analyzes the dynamic characteristics of broadband tristable energy harvesters to reveal their response mechanism via a bifurcation diagram, the corresponding frequency spectral analysis and the phase portrait topology. The bifurcation diagram of response voltages shows that tristable energy harvesters orderly undergoes singly periodic intrawell oscillation, singly periodic interwell oscillation, triply periodic interwell oscillation, singly periodic interwell oscillation, double-periodic interwell oscillation, chaotic oscillation, singly periodic interwell oscillation, multi-period oscillation, and finally enters into chaotic oscillation range, as the increase of the excitation amplitude. The frequency spectral analysis demonstrates that sub-harmonics and super-harmonics numerically and experimentally exist in the response voltages of tristable energy harvesters. In addition, it is found that both the first harmonic and the third harmonic are main frequency components in the response voltages.

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Liu, Jie, Chengye Wang, and Wenchao Wu. "Research on Meshing Stiffness and Vibration Response of Pitting Fault Gears with Different Degrees." International Journal of Rotating Machinery 2020 (February 1, 2020): 1–7. http://dx.doi.org/10.1155/2020/4176430.

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In order to study the influence of pitting on meshing stiffness, the normal distribution function is used to simulate the pitting location of pitting gear, and the potential energy method is used to analyze the influence of pitting on meshing stiffness. At the same time, the meshing stiffness of pitting gears with different degrees is analyzed by finite element method, and the validity of the calculation results with potential energy method is verified. On the basis of meshing stiffness, the dynamic model of gear system is established, and the vibration response of pitting gear system with different degrees is analyzed. The results show that with the increase of pitting area, the meshing stiffness decreases; the closer the meshing area of the driving wheel is to the pitting line, the more the meshing stiffness decreases, resulting in the intensification of vibration response and periodic impact; and in the time history diagram, there is a small spurious frequencies near the meshing frequency; in the phase diagrams and the Poincare diagram, trajectory and discrete point aggregation area is gradually increased.

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Radin, V. P., E. V. Poznyak, V. P. Chirkov, and O. V. Novikova. "Dynamic characteristics and adjustment of vibration isolators using the bilinear hysteresis." Proceedings of Higher Educational Institutions. Маchine Building, no. 12 (753) (December 2022): 14–23. http://dx.doi.org/10.18698/0536-1044-2022-12-14-23.

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The paper considers dynamic characteristics of a vibration protection device with bilinear deformation diagram and hysteresis behavior as part of a system with one degree of freedom. Based on results of the numerical simulation of the system’s response to harmonic effects, the amplitude-frequency characteristics (AFC) of relative displacements and absolute accelerations were constructed. AFC dependences on the limiting elastic displacement and the ratio of the diagram sections stiffness were studied. Based on the AFC, best parameters of a bilinear vibration isolator were determined to reduce the system dynamic response; besides, the nonlinear system resonant frequencies and the damping frequency regions were found.

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Yen, Nai‐chyuan, Louis R. Dragonette, and Christopher A. Ross. "Vein diagram: A simplified version of time‐frequency display for acoustic structure response." Journal of the Acoustical Society of America 92, no. 4 (October 1992): 2474. http://dx.doi.org/10.1121/1.404435.

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Gong, Jinzhe, Aaron C. Zecchin, Angus R. Simpson, and Martin F. Lambert. "Frequency Response Diagram for Pipeline Leak Detection: Comparing the Odd and Even Harmonics." Journal of Water Resources Planning and Management 140, no. 1 (January 2014): 65–74. http://dx.doi.org/10.1061/(asce)wr.1943-5452.0000298.

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Mu, Ying Cai. "Dynamic Response Analysis for Space Grid Structure with Different Boundary Conditions." Applied Mechanics and Materials 275-277 (January 2013): 972–76. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.972.

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Through the ansys software, we analysised the space truss structures for its dynamic response and observed its formation of frequency diagram . Based on the analysis of the observation ,natural vibration rules of the space truss structure are discussed. In the process of analysis, We got the conclusions of the support conditions of the change and support amount of adjustment to the influence of the space truss structure vibration frequency.

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Dhupia, Jaspreet S., Bartosz Powalka, A. Galip Ulsoy, and Reuven Katz. "Effect of a Nonlinear Joint on the Dynamic Performance of a Machine Tool." Journal of Manufacturing Science and Engineering 129, no. 5 (April 17, 2007): 943–50. http://dx.doi.org/10.1115/1.2752830.

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This paper presents the effect of experimentally evaluated nonlinearities in a machine joint on the overall machine tool dynamic performance using frequency response functions and stability lobe diagrams. Typical machine joints are very stiff and have weak nonlinearities. The experimental evaluation of the nonlinear joint parameters of a commercial translational guide has been discussed in Dhupia et al., 2007, J. Vibr. Control, accepted. Those results are used in the current paper to represent the connection between the column and the spindle of an idealized column-spindle machine structure. The goal is to isolate and understand the effects of such joints on the machine tool dynamic performance. The nonlinear receptance coupling approach is used to evaluate the frequency response function, which is then used to evaluate the stability lobe diagrams for an idealized machine structure. Despite the weak nonlinearities in the joint, significant shifts in the natural frequency and amplitudes at resonance can be observed at different forcing amplitudes. These changes in the structural dynamics, in turn, can lead to significant changes in the location of chatter stability lobes with respect to spindle speed. These variations in frequency response function and stability lobe diagram of machine tools due to nonlinearities in the structure are qualitatively verified by conducting impact hammer tests at different force amplitudes on a machine tool.

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Zhou, Wei, and Bao Bin Liu. "The Application of Frequency Response Analysis in Online Testing System of Transformer." Advanced Materials Research 571 (September 2012): 696–700. http://dx.doi.org/10.4028/www.scientific.net/amr.571.696.

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Online testing system based on frequency response analysis is proposed for the deformation of transformer winding. The structure of testing system, the selection of sweep sequence and computer diagram of data acquisition system are developed in the course of design. In the process of analysis, the concept of correlation coefficient is introduced to judge the relationship between the deformation extent and correlation coefficient. With the proposed method, the location of deformation can be determined. The testing curves demonstrate the effectiveness of the presented system.

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Rohani Bastami, Abbas, and Amir Bashari. "Rolling element bearing diagnosis using spectral kurtosis based on optimized impulse response wavelet." Journal of Vibration and Control 26, no. 3-4 (September 24, 2019): 175–85. http://dx.doi.org/10.1177/1077546319877702.

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Envelope analysis is widely used in fault diagnosis of rolling element bearings (REBs). In envelope analysis, it is necessary to select a frequency band which is related to the resonance of the bearing. Spectral kurtosis (SK) is known as a powerful method to find the resonance band in vibration of a defective REB. SK, calculated by short time Fourier transform, suffers from its dependency on the window length. In this article, a special wavelet transform is used to obtain a SK diagram. It is shown that choice of mother wavelet function has great influence on the resulting SK diagram. The proposed wavelet is based on the impulse response of a damped single degree of freedom system. An optimization algorithm is used to optimize the SK diagram for fault detection. The method is tested for both simulated and experimental vibration data.

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Siri, K., I. Batarseh, and C. Q. Lee. "Frequency response for the conventional parallel resonant converter based on the state-plane diagram." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 40, no. 1 (1993): 33–42. http://dx.doi.org/10.1109/81.215343.

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Peeters, Bart, Herman Van der Auweraer, Patrick Guillaume, and Jan Leuridan. "The PolyMAX Frequency-Domain Method: A New Standard for Modal Parameter Estimation?" Shock and Vibration 11, no. 3-4 (2004): 395–409. http://dx.doi.org/10.1155/2004/523692.

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Recently, a new non-iterative frequency-domain parameter estimation method was proposed. It is based on a (weighted) least-squares approach and uses multiple-input-multiple-output frequency response functions as primary data. This so-called “PolyMAX” or polyreference least-squares complex frequency-domain method can be implemented in a very similar way as the industry standard polyreference (time-domain) least-squares complex exponential method: in a first step a stabilisation diagram is constructed containing frequency, damping and participation information. Next, the mode shapes are found in a second least-squares step, based on the user selection of stable poles. One of the specific advantages of the technique lies in the very stable identification of the system poles and participation factors as a function of the specified system order, leading to easy-to-interpret stabilisation diagrams. This implies a potential for automating the method and to apply it to “difficult” estimation cases such as high-order and/or highly damped systems with large modal overlap. Some real-life automotive and aerospace case studies are discussed. PolyMAX is compared with classical methods concerning stability, accuracy of the estimated modal parameters and quality of the frequency response function synthesis.

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Qian, Youhua, and Wenjing Meng. "Mixed-Mode Oscillation in a Class of Delayed Feedback System and Multistability Dynamic Response." Complexity 2020 (February 6, 2020): 1–18. http://dx.doi.org/10.1155/2020/4871068.

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In this paper, a class of two-parameter mixed-mode oscillation with time delay under the action of amplitude modulation is studied. The investigation is from four aspects. Firstly, a parametric equation is considered as a slow variable. By the time-history diagram and phase diagram, we can find that the system generates a cluster discovery image. Secondly, the Euler method is used to discrete the system and obtain the discrete equation. Thirdly, the dynamic characteristics of the system at different time scales are discussed when the ratio of the natural frequency and the excitation frequency of the system is integer and noninteger. Fourthly, we discuss the influence of time delay on the discovery of clusters of this kind of system. The research shows that the time lag does not interfere with the influence of the cluster image, but the dynamics of the upper and lower parts of the oscillation in each period will be delayed. So, we can improve peak performance by adjusting the time lag and obtain the desired peak. Finally, we explore the multistate dynamic response of a two-dimensional nonautonomous Duffing system with higher order. According to bifurcation diagram and time-history curve, bistable state will appear in the system within the critical range. With the gradual increase of parameters, the chaotic attractor will suddenly disappear which will lead to the destruction of the bistable state.

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Dong, Hao, Yue Bi, Zhen-Bin Liu, and Xiao-Long Zhao. "Establishment and analysis of nonlinear frequency response model of planetary gear transmission system." Mechanical Sciences 12, no. 2 (December 17, 2021): 1093–104. http://dx.doi.org/10.5194/ms-12-1093-2021.

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Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

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Yanenko, Oleksii, and Leonid Virchenko. "SELECTIVE HIGH-SENSITIVITY RADIOMETER SWITCHING FREQUENCY AMPLIFIER WITH FREQUENCY RESPONSE TEMPERATURE COMPENSATION." Bulletin of Kyiv Polytechnic Institute. Series Instrument Making, no. 62(2) (December 24, 2021): 88–95. http://dx.doi.org/10.20535/1970.62(2).2021.249163.

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Problems. It is noted that the measurement of low-intensity microwave signals of various physical bodies and biological objects is associated with the need to provide high sensitivity, which can reach 10-14 -10-15 watts. The authors of the article studied the selective (selective) filter-amplifier of the switching frequency of the high-sensitivity modulation radiometer as one of the elements that have a significant impact on the sensitivity and accuracy of measurement, and developed recommendations for improving the stability of its parameters. The purpose of the research. The peculiarities of the modulation radiometer conversion channel operation are considered and the role of the selective switching frequency amplifier in providing such sensitivity is determined. The input and output signals of the selective amplifier, their relationship and the effect on the sensitivity of the radiometer were obtained and analyzed. The necessity of application of compensation of influence of temperature on characteristics of the filter taking into account temperature coefficients of elements of the scheme is proved. Conclusions. Modeling of a selective amplifier with a third-order filter was performed, the amplitude-frequency characteristic and the zone of its possible displacement at the maximum operating temperature were obtained. The structural and schematic diagram of the selective amplifier with automatic consideration of temperature influences, due to the introduction of feedback and correction of the frequency response of the filter has been developed. The main parameters of the bandpass filter built on the feedback circuit are determined. The use of a field-effect transistor channel connected in series with the resistors of the frequency-forming circuits of the third-order filter is proposed as an element of frequency response correction. The technical requirements for modeling and development of a selective amplifier are determined, which provide opportunities for implementation in practice. The research can be used to build a highly sensitive radiometric system for measuring low-intensity signals in areas such as biology and medicine.

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Lee, Pedro J., John P. Vítkovský, Martin F. Lambert, Angus R. Simpson, and James A. Liggett. "Leak location using the pattern of the frequency response diagram in pipelines: a numerical study." Journal of Sound and Vibration 284, no. 3-5 (June 2005): 1051–73. http://dx.doi.org/10.1016/j.jsv.2004.07.023.

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BAEK, SEUNG-JIN, SANG BONG LEE, and HYUNG JIN SUNG. "Response of a circular cylinder wake to superharmonic excitation." Journal of Fluid Mechanics 442 (August 24, 2001): 67–88. http://dx.doi.org/10.1017/s0022112001004980.

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A systematic numerical analysis is performed for superharmonic excitations in a wake where a circular cylinder is rotationally oscillated in time. Emphasis is placed on identifying the secondary and tertiary lock-on in the forced wakes. The frequency responses are scrutinized by measuring the lift coefficient (CL). A direct numerical simulation has been conducted to portray the unsteady dynamics of wake flows behind a circular cylinder. The Reynolds number based on the diameter is Re = 106, and the forcing magnitude is 0.10 [les ] Ωmax [les ] 0.40. The tertiary lock-on is observed, where the shedding frequency (St0) is one third of the forcing frequency (Sf), i.e. the 1/3 subharmonic lock-on. The phase shift of CL with respect to the forcing frequency is observed. It is similar to that of the primary lock-on. However, in the secondary superharmonic excitation, modulated oscillations are observed, i.e. the lock-on does not exist. As Ωmax increases, St0 is gradually shifted from the natural shedding frequency (St*0) to lower values. The magnitudes and phases of Sf and St0 are analysed by the phase diagram. The vorticity contours are employed to examine the vortex formation mode against the forcing conditions.

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Qian, Bo, Shi Jing Wu, Hong Wu Li, and Jin Xu. "The Research on Nonlinear Vibration Characteristic of Ravingneaux Compound Planetary Gear Sets." Applied Mechanics and Materials 105-107 (September 2011): 62–69. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.62.

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The nonlinear dynamic model of Ravingneaux compound planetary gear sets has been built. The model includes time-varying mesh stiffness of gears, backlash as well as comprehensive mesh errors nonlinearities. By introducing relative displacements of components as the new generalized coordinates, uniform nonlinear differential equations of compound planetary gear sets are built. Then the nondimensional dynamic differential equations are derived. The nonlinear differential equations have been solved utilizing ariable step size Gill method. By changing system nondimensional excitation frequency, monocycle anharmonic response, multiply periodic subharmonic response, quasi-periodic response and chaotic response are obtained. By means of time histories, phase-plane diagram, Poincare maps and power spectrum, various responses are compared and analyzed in detail.

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Yu, M. C., X. Gao, and Q. Chen. "Nonlinear Frequency Response Analysis and Jump Avoidance Design of Molecular Spring Isolator." Journal of Mechanics 32, no. 5 (July 14, 2016): 527–38. http://dx.doi.org/10.1017/jmech.2016.52.

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AbstractMolecular spring vibration isolation technology has been invented in the recent years but it still needs further development in dynamics theory. A molecular spring isolation (MSI) consists of water and hydrophobic zeolites as working medium, providing high-static-low-dynamic stiffness. The dynamic properties of MSI are thoroughly investigated in this paper. Firstly, the nonlinear dynamic model of a vibration system support by MSI, i.e. the equation of motion, is established. Then the averaging method is employed to estimate the frequency response function (FRF) of the primary resonance. The phase trajectories diagram evolvement of primary resonance is also investigated to analysis the stability of the primary resonance response. From the plot of FRF, it is found that there exists a jump phenomenon induced by nonlinear stiffness, which may have harmful impacts on the equipment which is supposed to be protected from vibrations and shocks. To avoid jump, the FRF is analyzed to find the critical values of system parameters and a jump avoidance criterion is introduced.

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Xiao, Jin Zhuang, Rui Jing Xue, and Hong Rui Wang. "Integration Frequency Response of Human Dynamic Anterior-Posterior Balance under Passive Motion Stimulus." Applied Mechanics and Materials 644-650 (September 2014): 3956–59. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.3956.

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In order to study the frequency characteristic of body oscillation in the anterior-posterior (AP) direction during upright stance, 10 subjects were exposed to the motion platform with specific posture and followed the tracks of the passive motion stimulus, sinusoidal waveform, with the increasing frequencies (0.05-1.2Hz). By measuring the displacement of the center of gravity (COG), the bode diagram between the motion of platform and body’s COG was obtained. Results showed that the mean cut-off frequency (COF) is 0.5 Hz, the mean resonance frequency (RF) is 0.316 Hz and the bandwidth of the body oscillation is 0.1-0.5 Hz in AP direction. In a conclusion, this study reaches the frequency response of human dynamic balance under passive motion stimulus by using COG values, proposes a method based on the COF values to evaluate the balance ability, and provides data support for the research of balance ability in the medical community.

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Iwaniec, Joanna, Grzegorz Litak, Marek Iwaniec, Jerzy Margielewicz, Damian Gąska, Mykhaylo Melnyk, and Wojciech Zabierowski. "Response Identification in a Vibration Energy-Harvesting System with Quasi-Zero Stiffness and Two Potential Wells." Energies 14, no. 13 (June 30, 2021): 3926. http://dx.doi.org/10.3390/en14133926.

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In this paper, the frequency broadband effect in vibration energy harvesting was studied numerically using a quasi-zero stiffness resonator with two potential wells and piezoelectric transducers. Corresponding solutions were investigated for system excitation harmonics at various frequencies. Solutions for the higher voltage output were collected in specific branches of the power output diagram. Both the resonant solution synchronized with excitation and the frequency responses of the subharmonic spectra were found. The selected cases were illustrated and classified using a phase portrait, a Poincaré section, and recurrence plot (RP) approaches. Select recurrence quantification analysis (RQA) measures were used to characterize the discussed solutions.

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Sepehrinour, M., and M. Nezami. "Dynamic Response of an Electro-Rheological Sandwich Beam with Different Elastic Layers Subjected to Simultaneous Impact Loads." Applied Mechanics and Materials 232 (November 2012): 117–21. http://dx.doi.org/10.4028/www.scientific.net/amm.232.117.

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Dynamic response of an electro-rheological sandwich beam subjected to simultaneous Impact loads will be considered. Analytical solution will be used to draw FRF diagram of the beam for different electric field. Upper and lower layers of the beam have different material properties. Coupled governing equations derived from Hamilton Principle will be solved in frequency domain to find transverse vibration of the beam.

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Xie, Xuan, Ming Li, and Junwei Wang. "Nonlinear vibration behaviors of marine rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion." Advances in Mechanical Engineering 13, no. 12 (December 2021): 168781402110673. http://dx.doi.org/10.1177/16878140211067367.

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To study the nonlinear vibration behaviors of rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion, the dynamic model is established considering the effect of heaving motion, its steady-state responses are numerically obtained using Runge-Kutta method and the results are surveyed by tools such as the spectrum waterfall diagram, time-domain response, frequency-domain response, axis orbit, and Poincaré map. The effects of rotating speed, ship heaving amplitude, and its frequency on the nonlinear dynamic behavior of the system are mainly studied. The results show that the responses of the rotor and raft are of obvious nonlinear behaviors such as amplitude jumping, bifurcation, and chaos due to the effects of nonlinear oil film force and ship heaving motion. With the increase of rotating speed, the motion of rotor and raft presents quasi-periodic and chaotic vibrations. Ship heaving amplitude and its frequency all have great effect on the vibration of rotor and raft; as heaving amplitude or frequency increases, the motion state of rotor and raft changes, and the amplitude of raft increases significantly. The displacement restrictor can effectively limit the vibrating displacements of the raft when ship heaving amplitude or its frequency is large.

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Yuda, Hu, Li Zhe, Du Guojun, and Wang Yanan. "Magneto-Elastic Combination Resonance of Rotating Circular Plate with Varying Speed Under Alternating Load." International Journal of Structural Stability and Dynamics 18, no. 03 (February 27, 2018): 1850032. http://dx.doi.org/10.1142/s0219455418500323.

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Nonlinear magneto-elastic combined resonance of parametric and forced excitations is investigated for a rotating circular plate with a variable speed under alternating load. According to the magneto-elastic vibration equations of a conductive rotating thin circular plate, the axisymmetric vibration differential equations of the rotating circular plate under transverse magnetic field are obtained through the application of the Galerkin integral method. The method of multiple scales is applied to solve the differential equations of the circular plate under alternating magnetic field, and the resonance states of the system under combined parametric and forced excitations are obtained by analyzing secular terms. The respective amplitude–frequency response equations are also derived, as well as the necessary and sufficient conditions of the system to make it stable. A numerical method is adopted to acquire amplitude–frequency response curves, bifurcation diagrams of amplitude and the variation pattern of amplitude with magnetic induction intensity and radial force. The influence of parameter variation on stability of the system is also investigated. Based on the global bifurcation diagram of the system, the influence of the change of bifurcation parameters on the system dynamics is discussed.

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Onsorynezhad, Saeed, Amin Abedini, and Fengxia Wang. "Parametric optimization of a frequency-up-conversion piezoelectric harvester via discontinuous analysis." Journal of Vibration and Control 26, no. 15-16 (January 14, 2020): 1241–52. http://dx.doi.org/10.1177/1077546319894797.

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In this study, the dynamical and electrical behaviors of an impact-based frequency-up-conversion energy harvester were studied based on discontinuous dynamics theory. This analytical study enables us to better understand the response of an impact-based frequency-up-conversion energy harvester as system parameters change, hence, guiding us to design a high-efficiency energy harvester via optimizing the values of the critical parameters of the system. For a given base excitation, the optimum gap to maximize the output power was obtained. The energy harvester consists of a sinusoidal vibrating piezoelectric bimorph and a stopper. The equations of the piezoelectric bimorph, which was modeled as an Euler–Bernoulli beam, were obtained based on the linear piezoelectric constitutive law. The generated voltage and power of the energy harvester were obtained via discontinuous dynamics analysis. Furthermore, the bifurcation diagrams of period-1 and period-2 motions were presented as the excitation frequency varying. To better understand the effect of different parameters on the performance of our system, the bifurcation trees of the period-1 motion versus varying excitation frequency were analytically obtained for different initial gap distances between the piezoelectric beam and the stopper. In addition, the bifurcation diagram of period solutions with a constant excitation frequency and varying gap distance was also attained.

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Mao, Hancheng, Guangbin Yu, Wei Liu, and Tiantian Xu. "Out-of-Plane Free Vibration and Forced Harmonic Response of a Curved Beam." Shock and Vibration 2020 (December 29, 2020): 1–14. http://dx.doi.org/10.1155/2020/8891585.

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Based on the governing differential equation of out-of-plane curved beam, the wave propagation behavior, free vibration, and transmission properties are presented theoretically in this paper. Firstly, harmonic wave solutions are given to investigate the dispersion relation between frequency and wave number, cut-off frequency, displacement, amplitude ratio, and phase diagram. The frequency spectrum results are obtained to verify the work by Kang and Lee. Furthermore, natural frequencies of the single and composite curved beam are calculated through solving the characteristic equation in the case of free-free, clamped-clamped, and free-clamped boundaries. Finally, the transfer matrices of the out-of-plane curved beam are derived by combining the continuity between the different interfaces. The transmissibility curves of the single and composite curved beam are compared to find the vibration attention band. This work will be valuable to extend the study of the out-of-plane vibration of curved beams.

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Li, Zhongqun, Zhikang Wang, and Xiaofang Shi. "Fast prediction of chatter stability lobe diagram for milling process using frequency response function or modal parameters." International Journal of Advanced Manufacturing Technology 89, no. 9-12 (January 12, 2017): 2603–12. http://dx.doi.org/10.1007/s00170-016-9959-4.

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Zhu, Rui, Qingguo Fei, Dong Jiang, and Xiaochen Hang. "Using Sherman–Morrison theory to remove the coupled effects of multi-transducers in vibration test." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 4 (January 18, 2018): 1364–76. http://dx.doi.org/10.1177/0954410017753805.

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Modal parameter identification is adversely affected by the mass loading of the transducer in experiments, especially when multi-transducers are arranged on the lightweight structure. In order to remove the coupling effects of transducers on each measurement point, a hierarchical multi-transducers eliminations method based on Sherman–Morrison theory is investigated. The method consists of two steps: (1) Decomposition: multiple elimination is decomposed into multi-levels, the relationship of the frequency response functions between each level is illustrated in the tree diagram; (2) Elimination: according to the relationship between each level, the measured frequency response functions are modified level by level. Numerical simulation is conducted by employing a three-degrees-of-freedom spring-mass system and the robustness is verified in the noise case. Experimental investigations are undertaken by employing a lightweight cantilever beam: Laser Doppler vibrometer is adopted to obtain measured frequency response functions without transducer mass loading effect, which are regarded as the target data. The initial frequency response functions are obtained in the case, in which multi-accelerometers are arranged and the effects should be removed. The result shows that the method can effectively decouple the frequency response functions due to transducers. In the elimination process, it is necessary to delete duplicate information (frequency response functions), which can greatly reduce the amount of calculation. And the effects of multi-transducers mass can be removed and the corrected frequency response functions are in quite good agreement with the target values.

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Luo, Hai Tao, Yu Wang Liu, Hong Guang Wang, and Wei Jia Zhou. "Nonlinear Vibration Analysis of Machine-Tool Guideway System with Clearance." Advanced Engineering Forum 2-3 (December 2011): 661–66. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.661.

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This paper studies hysteretic effect of machine-tool guideway system with clearance, establishes the nonlinear dynamics model of guideway system with symmetric clearance, and obtains the equivalent damping and equivalent stiffness coefficients using asymptotic method. With the use of time-domain graph, frequency-domain graph, phase trajectory figure, Poincare section figure, bifurcation diagram, and lyapunov exponent figure, the dynamics response of damping and external vibration frequency effect on system is studied. The result shows that the period, double-period and chaos movement will occur when the system parameters change in certain range.

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Han, Jianxin, Lei Li, Gang Jin, Jingjing Feng, Baizhou Li, Haili Jia, and Wenkui Ma. "Vibration Identification of Folded-MEMS Comb Drive Resonators." Micromachines 9, no. 8 (August 1, 2018): 381. http://dx.doi.org/10.3390/mi9080381.

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Natural frequency and frequency response are two important indicators for the performances of resonant microelectromechanical systems (MEMS) devices. This paper analytically and numerically investigates the vibration identification of the primary resonance of one type of folded-MEMS comb drive resonator. The governing equation of motion, considering structure and electrostatic nonlinearities, is firstly introduced. To overcome the shortcoming of frequency assumption in the literature, an improved theoretical solution procedure combined with the method of multiple scales and the homotopy concept is applied for primary resonance solutions in which frequency shift due to DC voltage is thoroughly considered. Through theoretical predictions and numerical results via the finite difference method and fourth-order Runge-Kutta simulation, we find that the primary frequency response actually includes low and high-energy branches when AC excitation is small enough. As AC excitation increases to a certain value, both branches intersect with each other. Then, based on the variation properties of frequency response branches, hardening and softening bending, and the ideal estimation of dynamic pull-in instability, a zoning diagram depicting extreme vibration amplitude versus DC voltage is then obtained that separates the dynamic response into five regions. Excellent agreements between the theoretical predictions and simulation results illustrate the effectiveness of the analyses.

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Du, Heng, Jian Xin Lin, Fan Guo, and Chong Ma. "The Design of a Novel High Frequency Digital Valve Based on Rotating and Differentially Parallel Control." Applied Mechanics and Materials 602-605 (August 2014): 1317–23. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1317.

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Due to the ability of the strong anti-interference and directly digital controlling, digital valve has great applications and developing potential in the filed of high frequency response digital servo valve. Base on the rotating structure, a novel high frequency digital valve which can be rotated and controlled in differential parallel way is designed, and the frequency characteristic of electrical signals converting into rotation signals is developed through differential and parallel control of valve spool and valve sleeve. Meanwhile, the hydraulic natural frequency of servo-screw mechanism is further enhanced by the control way of hydraulic half-bridge type A in both chambers of valve spool, and corresponding mathematical model and control block diagram are built. Theoretical analysis concludes that the frequency response characteristic of digital valve is developed significantly. In addition, the multi-gain of rotation angle and axial displacement of valve spool is realized through milling the spiral grooves with different helix angles in the inside of valve sleeve, which improves the flow adaptability of high frequency digital valve effectively. Compared to traditional rotary digital valve, the designed novel digital valve that can be controlled by rotating differentially and parallel has greater advantages in high frequency response and flow adaptability, it provides a new scheme for engineering applications of high frequency digital valve.

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Jamri, M. Saifuzam, Muhammad Nizam Kamarudin, and Mohd Luqma Mohd Jamil. "An investigation of inertia constant in single generator on transient analysis for an isolated electrical network system." Indonesian Journal of Electrical Engineering and Computer Science 23, no. 3 (September 1, 2021): 1299. http://dx.doi.org/10.11591/ijeecs.v23.i3.pp1299-1305.

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<p>An isolated electrical network which fed by an independent generator for a low voltage system is considerable in remote and islandic areas. Although the network system has less complexity in term of system structure, its stability level is crucial due to frequency dynamical responses. An influence of initial stability margin on frequency stability study during contingency situation is a thing rather than being ignored. Here the initial transient response inherently delivers important info such as system inertia and momentarily power deficit. In this paper, an investigation of transient stability responses under different inertia values is carried out. The investigation is carried out by modelling the isolated system in MATLAB/Simulink environment which consists of state-space mathematical equations. It is confirmed that the generator system inertia shapes the initial slope, speed droop and oscillation. For a verification purpose, the influence of system inertia is also analyzed using bode diagram in which system gain and frequency margin are evaluated.</p><p> </p>

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Liu, Hong, and Guo Zhu Zhao. "Two Methods to Test Transducer Array Directivity." Advanced Materials Research 912-914 (April 2014): 1485–88. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1485.

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An array which possess more array element number and whose frequency of the drive signal can be as large as possible in a range, directivity will be more preferable. On the other hand, when the structure of the sound radiating surface of the transducer or array layout is symmetrical, the corresponding directivity pattern will be symmetrical. In order to test transducer directivity, two methods are designed. The one is to measure the ultrasonic sound pressure level by instruments. The sound pressure level is measured at multiple points to deduce the directivity angle of the acoustic transducer array. The beam width of the 3×3 array is about at 23kHz, and the directivity acute angle is about 10°; higher frequencies will lead to the side lobes, but it can be negligible when compared to the main lobe. The other method is using the frequency analyzer to test transducer directivity in a silencer chamber. The sound pressure level can be read out from frequency response diagrams. The angle between the sound pressure value that decreasing 3db from the max value 111.7db and the max value is about 11°. So the directivity acute angle is about 11°. It should be noticed that, as the directivity diagram can not be directly attributed, there is some deviation in the conclusion.

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Blekhman, I., and E. Kremer. "Stochastic resonance as the averaged response to random broadband excitation and its possible applications." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 23-24 (April 23, 2019): 7476–88. http://dx.doi.org/10.1177/0954406219842283.

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Within the framework of vibrational mechanics, a stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point was considered and the dynamic properties of its averaged motion were studied. It is shown that, unlike the ordinary Stephenson–Kapitsa pendulum with deterministic vertical oscillations of the suspension point, both an increase and a decrease in the effective natural frequency are possible under the influence of high-frequency stochastic oscillations. A formula is derived for the amplitude of low-frequency oscillations as a function of the intensity of high-frequency stochastic oscillations and the possibility of a stochastic resonance in this system is shown. The dependence of the stochastic resonance on the mass and the damping coefficient is analyzed. It is shown that the points of the stochastic resonance lie in the plane of parameters “intensity of stochastic excitation” and “amplitude of low-frequency oscillation” on a universal curve that is independent of the mass of the pendulum. Peculiar self-oscillations in a system for which stochastic oscillations are produced by a technological load and, therefore, depend monotonically on the amplitude of low-frequency oscillations are discussed. A schematic diagram of these phenomena is proposed. The motion of the machine is described by the same equations as the stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point. A strategy of control for such a vibro-machine is proposed with the aim of maintaining it at resonance and providing an energetically efficient mode of operation.

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Barrios Sánchez, Jorge Manuel, Roberto Baeza Serrato, and Marco Bianchetti. "Design and Development of a Mathematical Model for an Industrial Process, in a System Dynamics Environment." Applied Sciences 12, no. 19 (September 30, 2022): 9855. http://dx.doi.org/10.3390/app12199855.

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This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency domain based on the Laplace transform. The conventional control engineering technique is used to present and reduce the dynamic system in a block diagram as a mechanism for determining the structure of the system. The direct path equation and the feedback equation are determined to obtain mathematical models that explain the trajectory of the behavior of each state variable through a transfer function in response to the different inputs of the system. The research proposal is based on presenting an alternative of analytical validation for more robust decision-making to systems dynamics models, based on the explanation of the system structure through a transfer function and its analysis of stability and external controllability for the system dynamics model under study. The results are visually analyzed in a root diagram.

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Devia, D. F., F. Mesa, and D. M. Devia. "Physical implementation of optimal control over a direct current." Journal of Physics: Conference Series 2153, no. 1 (January 1, 2022): 012011. http://dx.doi.org/10.1088/1742-6596/2153/1/012011.

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Abstract In the next manuscript we will show an interesting physical application of the technique of optimal control over a direct current, more exactly on a direct current motor. For this, the mathematical support or scaffolding that allows to establish the model of the problem will be presented in the development of the document, which contains a basic structure supported in a general dynamic system (linear or non-linear) and an objective function that will depend on the system. Although in essence the optimal control problems correspond to infinite spaces, the finite-dimensional case will be analyzed initially and then made an extension to the case of a quadratic linear regulator for an interval of infinite duration. The results of the implementation of this optimal control technique on a direct current motor will be analyzed by means of Bole diagrams that will represent the frequency response of the system and a follow-up diagram of set points and rejection of disturbances.

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Tzanov, Vassil V., Bernd Krauskopf, and Simon A. Neild. "Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency." International Journal of Bifurcation and Chaos 24, no. 09 (September 2014): 1430024. http://dx.doi.org/10.1142/s0218127414300249.

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Inclined cables are essential structural elements that are used most prominently in cable-stayed bridges. When the bridge deck oscillates due to an external force, such as passing traffic, cable vibrations can arise not only in the plane of excitation, but also in the perpendicular plane. This undesirable phenomenon can be modeled as an auto-parametric resonance between the in-plane and out-of-plane modes of vibration of the cable. In this paper, we consider a three-mode model, capturing the second in-plane, and first and second out-of-plane modes, and use it to study the response of an inclined cable that is vertically excited at its lower (deck) support at a frequency close to the second natural frequency of the cable. Averaging is applied to the model and then the solutions and bifurcations of the resulting averaged differential equations are investigated and mapped out with numerical continuation. In this way, we present a detailed bifurcation study of the different possible responses of the cable. We first consider the equilibria of the averaged model, of which there are four types that are distinguished by whether each of the two out-of-plane modes is present or not in the cable response. Each type of equilibrium is computed and represented as a surface over the plane of amplitude and frequency of the forcing. The stability of the equilibria changes and different surfaces meet along curves of bifurcations, which are continued directly. Overall, we present a comprehensive geometric picture of the two-parameter bifurcation diagram of the constant-amplitude coupled-mode response of the cable. We then focused on bifurcating periodic orbits, which correspond to cable dynamics with varying amplitudes of the participating second in-plane and second out-of-plane modes. The range of excitation amplitude and frequency is determined where such whirling cable motion can occur. Further bifurcations — period-doubling cascades and a Shilnikov homoclinic bifurcation — are found that lead to a chaotic cable response. Whirling and chaotic cable dynamics are confirmed by time-step simulations of the full three-mode model. The different cable responses are characterized, and can be distinguished clearly, by their motion at the quarter-span and by their frequency spectra.

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Ying, Jiayang, Yinghou Jiao, and Zhaobo Chen. "Nonlinear Dynamics Analysis of Tilting Pad Journal Bearing-Rotor System." Shock and Vibration 18, no. 1-2 (2011): 45–52. http://dx.doi.org/10.1155/2011/213742.

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The nonlinear dynamics theory is increasingly applied in the dynamics analysis of tilting pad journal bearing-rotor system. However, extensive work on system dynamics done previously neglects the influence caused by the moment of inertia of the pad. In this paper, a comparison is made between the responses of the rotor in the bearings with and without pad inertia effect. Taking the Jeffcott rotor system as an example, the characteristics of bearing-rotor system, such as bifurcation diagram, cycle response, frequency spectrum, phase trajectories, and Poincaré maps, were attained within a certain rotation rate range. The pivotal oil-film force of tilting pad journal bearing was calculated by database method. The results directly demonstrate that considering the influence of the pad moment of inertia, system dynamics characteristics are found more complicated when rotor-bearing system works around natural frequency and system bifurcation is observed forward when rotor-bearing system works on high-speed range.

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Duan, Shiqiang, Hua Zheng, and Junhao Liu. "A Novel Classification Method for Flutter Signals Based on the CNN and STFT." International Journal of Aerospace Engineering 2019 (April 9, 2019): 1–8. http://dx.doi.org/10.1155/2019/9375437.

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Necessary model calculation simplifications, uncertainty in actual wind tunnel test, and data acquisition system error altogether lead to error between a set of actual experimental results and a set of theoretical design results; wind tunnel test flutter data can be utilized to feedback this error. In this study, a signal processing method was established to use the structural response signals from an aeroelastic model to classify flutter signals via deep learning algorithm. This novel flutter signal processing and classification method works by combining a convolutional neural network (CNN) with time-frequency analysis. Flutter characteristics are revealed in both time and frequency domains, which are harmonic or divergent in the time series; the flutter model energy is singular and significantly increases in the frequency view, so the features of the time-frequency diagram can be extracted from the dataset-trained CNN model. As the foundation of the subsequent deep learning algorithm, the datasets are placed into a collection of time-frequency diagrams calculated by short-time Fourier transform (STFT) and labeled with two artificial states, flutter or no flutter, depending on the source of the signal measured from a wind tunnel test on the aeroelastic model. After preprocessing, a cross-validation schedule is implemented to update (and optimize) CNN parameters though the trained dataset. The trained models were compared against test datasets to validate their reliability and robustness. Our results indicate that the accuracy rate of test datasets reaches 90%. The trained models can effectively and automatically distinguish whether or not there is flutter in the measured signals.

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Yin, Yilin, Zhenghong Yang, and Meilun Shi. "Analytical Expression of Complex Modulus for Viscoelastic Material." International Journal of Applied Mechanics 12, no. 05 (June 2020): 2050048. http://dx.doi.org/10.1142/s1758825120500489.

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Transfer functions in the linear dynamic system theory are applied to characterize dynamic mechanical properties of viscoelastic materials. Correlation between transfer functions and typical rheological models and fractional derivative ones are briefly introduced. The transfer function of a rheological model may be expressed in terms of multiplication of factored polynomials. The frequency–response data are presented in the form of a Bode plot of magnitude, from which a transfer function can be established. The characteristic times can be conveniently identified via the corner frequencies of asymptotes of the magnitude curve. Dynamic frequency sweep results for a typical viscoelastic solid are presented to illustrate the use of the Bode diagram method for parameter identification.

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Cheng, Zhenbang, Kang Huang, Yangshou Xiong, and Meng Sang. "Dynamic Analysis of a High-Contact-Ratio Spur Gear System with Localized Spalling and Experimental Validation." Machines 10, no. 2 (February 18, 2022): 154. http://dx.doi.org/10.3390/machines10020154.

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The dynamic characteristics and tooth spalling fault features are studied for the high-contact-ratio spur gear bearing system. The bending torsional dynamic model is proposed in this study for the gear bearing system with an ellipsoid spalling fault. This model also considers time-varying meshing stiffness, tooth friction, fractal gear backlash, and comprehensive transmission error. The meshing stiffness of the system is evaluated using the potential energy method. The bifurcation diagram, time-domain waveform, Poincaré map, phase map, frequency spectrum, and related three-dimensional map are used as tools to analyze the system’s dynamic response qualitatively. The results reveal that the system’s motion with ellipsoid tooth spalling defect exhibits rich dynamic behavior. The response of the proposed dynamic model is consistent with experimental results in the frequency domain. Therefore, the developed dynamic model can predict the system’s vibration behavior with localized spalling fault. Hence, it could also provide a theoretical foundation for future spall defect diagnosis of the gear transmission system.

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QIN, WEIYANG, and GUANG MENG. "NONLINEAR DYNAMIC RESPONSE AND CHAOS OF A CRACKED ROTOR WITH TWO DISKS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3425–36. http://dx.doi.org/10.1142/s021812740300865x.

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In this paper, the nonlinear response and chaos of a cracked rotor with two disks are studied. Considering the breadth of crack in one rotor revolution, the motion equations of the system are derived and then solved. The results show that the rotor response is sensitive to the crack depth, rotating speed, damping ratio and imbalance. When a crack occurs, the frequency of swing vibration is a multiple of rotating speed (NΩ,N=2,3,…). There are three main routes for response to chaos, that is from quasi-periodic to chaos, from quasi-periodic to quasi-periodic bifurcation and then to chaos and the intermittence to chaos. The intermittence chaos occurs even for a small crack. With the intermittence chaos range there exists the periodic-doubling bifurcation with time. Larger imbalance parameter and damping ratio can suppress chaos. The diagram of time-phase is a useful way to analyze the nonlinear response.

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Simpson, T. A., and R. A. Ibrahim. "Nonlinear Friction-Induced Vibration in Water-Lubricated Bearings." Journal of Vibration and Control 2, no. 1 (January 1996): 87–113. http://dx.doi.org/10.1177/107754639600200106.

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The problem of friction-induced vibration and squeal in water-lubricated shipboard bearings has received extensive studies during the 1970s. These studies were dominated by experimental tests of section models that emulated the actual bearing dynamics. Linear analytical models were analyzed to predict stability boundaries of the equilibrium position. The role of nonlinearity due to the friction-speed curve as well as the time variation of the friction coefficient was not considered. The purpose of the present study is to develop and analyze a nonlinear two-degree-of-freedom model that emulates the dynamics of water-lubricated bearings. Different dynamic characteristics are predicted from the numerical simulation of the equations of motion. A bifurcation diagram is constructed and exhibits different regimes. These regimes include modulated response signals characterized by two frequency responses, on-off intermittent motion representing the incipient of squeal behavior, and limit cycles accompanied with high frequency components. The squeal is revealed by the presence of a high frequency vibration superimposed on the fundamental system frequency. The occurrence of each regime mainly depends on the value of the slope of the friction-speed curve. Other parameters such as natural frequencies, damping ratios, mass ratio, and the initial conditions have less influence on the incipient of squeal.

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Xuan, X. J., Z. H. Haung, K. D. Wu, and J. P. Hung. "Prediction of the Frequency Response Function of a Tool Holder-Tool Assembly Based on Receptance Coupling Method." Engineering, Technology & Applied Science Research 8, no. 6 (December 22, 2018): 3556–60. http://dx.doi.org/10.48084/etasr.2372.

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Regenerative chatter has a fatal influence on machine performance in high-speed milling process. Basically, machine condition without chattering can be selected from the stability lobes diagram, which is estimated from the tool point frequency response function (FRF). However, measurements of the tool point FRF would be a complicated and time-consuming task with less efficiency. Therefore prediction of the tool point FRF is of importance for further calculation of the machining stability. This study employed the receptance coupling analysis method to predict the FRF of a tool holder-tool module, which is normally composed of substructures, tool holder and cutter with different length. In this study, the angular components of FRFs of the substructures required for coupling operation were predicted by finite element analysis, apart from the translational components measured by vibration experiments. Using this method, the effects of the overhang length of the cutter on the dynamic characteristics have been proven and successfully verified by the experimental measurements. The proposed method can be an effective way to accurately predict the dynamic behavior of the spindle tool system with different tool holder-tool modules.

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Mustafa, Aalim M., Muhammad A. Hawwa, and David E. Hardt. "Vibration of an axially moving beam supported by a slightly curved elastic foundation." Journal of Vibration and Control 24, no. 17 (July 4, 2017): 4000–4009. http://dx.doi.org/10.1177/1077546317717886.

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The vibration of an axially moving beam following a slightly curved path was studied. The simply supported beam was travelling axially on a curved frictionless foundation with nonlinear elastic characteristics. The main objective of this work was to investigate the effect of the moving beam path curvature on its vibration, and the effect of different parameters on the system’s dynamic response. These parameters include axial speed, applied tension, and stiffness of the supporting foundation. A Galerkin decomposition approach with four-term truncation accuracy was used to realize a mathematical model that describes the dynamic behavior of the axially moving beam on a slightly curved foundation. Numerical solutions showed that the natural frequency of the axially moving beam travelling on the curved elastic support was higher than that of an axially moving straight beam for all cases considered of different path curvatures and different degrees of support stiffness. Forced vibrations of an axially moving beam on a curved elastic support were also considered under harmonic excitation. Bifurcation diagrams were obtained for the primary resonance excitation using the excitation amplitude as a controlling parameter, while keeping the excitation frequency fixed. It was found that the amplitude–frequency diagram for the axially moving beam on the curved path exhibited many types of bifurcations, including period doubling bifurcation, period four bifurcation and many jumps, compared to that of an axially moving beam resting on a straight elastic support.

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Vahedi, Hani, Abdolreza Sheikholeslami, Mohammad Tavakoli Bina, and Mahmood Vahedi. "Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and High-Frequency Harmonics." Advances in Power Electronics 2011 (June 28, 2011): 1–6. http://dx.doi.org/10.1155/2011/397872.

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Hysteresis Current Control (HCC) is widely used due to its simplicity in implementation, fast and accurate response. However, the main issue is its variable switching frequency which leads to extraswitching losses and injecting high-frequency harmonics into the system current. To solve this problem, adaptive hysteresis current control (AHCC) has been introduced which produces hysteresis bandwidth which instantaneously results in smoother and constant switching frequency. In this paper the instantaneous power theory is used to extract the harmonic components of system current. Then fixed-band hysteresis current control is explained. Because of fixed-band variable frequency disadvantages, the adaptive hysteresis current control is explained that leads to fixing the switching frequency and reducing the high-frequency components in source current waveform. Due to these advantages of AHCC, the switching frequency and switching losses will be diminished appropriately. Some simulations are done in MATLAB/Simulink. The Fourier Transform and THD results of source and load currents and the instantaneous switching frequency diagram are discussed to prove the efficiency of this method. The Fourier Transform and THD results of source and load currents are discussed to prove the validity of this method.

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Journal articles on the topic 'Frequency response diagram'

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