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Journal articles on the topic 'NONLINEAR RANDOM VIBRATION ANALYSIS'

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Author: Grafiati
Published: 11 September 2023

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1

Manohar, C. S. "Methods of nonlinear random vibration analysis." Sadhana 20, no. 2-4 (April 1995): 345–71. http://dx.doi.org/10.1007/bf02823196.

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2

HE, YONG, and WEI-LIANG JIN. "A STOCHASTIC EQUIVALENT LINEARIZATION FOR ANALYSIS OF MULTIPLE-DEGREE-OF-FREEDOM FLEXIBLE STRUCTURES." Journal of Earthquake and Tsunami 03, no. 04 (December 2009): 291–303. http://dx.doi.org/10.1142/s1793431109000640.

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Stochastic equivalent linearization (SEL) method has gained wide popularity because of its versatility in application to multiple-degree-of-freedom (MDOF) nonlinear systems. It is restricted in the random vibration analysis of flexible structures because of the implicit nonlinear system. This paper presents a new method for the equivalent nonlinear system of flexible structures. Using this method, the implicit geometrically nonlinear system can be represented as an explicit equivalent nonlinear system. According to the modal analysis method, the geometrically nonlinear force is replaced by a high-order moment of modal coordinate. The MDOF physical system is translated into a modal system, which could be solved easily. Based on the equivalent nonlinear system, the nonlinear random vibration method is presented by using SEL technology. By using the pseudo-excitation method, the efficiency of the nonlinear random vibration method is increased obviously. The rapid calculation makes it possible to analyze the nonlinear random vibration of MDOF flexible structure. The validation shows that the method has reasonable precision and high efficiency and it could be used in the random vibration analysis of practical flexible structures.
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3

Cryns, Jackson W., Brian K. Hatchell, Emiliano Santiago-Rojas, and Kurt L. Silvers. "Experimental Analysis of a Piezoelectric Energy Harvesting System for Harmonic, Random, and Sine on Random Vibration." Advances in Acoustics and Vibration 2013 (August 4, 2013): 1–12. http://dx.doi.org/10.1155/2013/241025.

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Harvesting power with a piezoelectric vibration powered generator using a full-wave rectifier conditioning circuit is experimentally compared for varying sinusoidal, random, and sine on random (SOR) input vibration scenarios; the implications of source vibration characteristics on harvester design are discussed. The rise in popularity of harvesting energy from ambient vibrations has made compact, energy dense piezoelectric generators commercially available. Much of the available literature focuses on maximizing harvested power through nonlinear processing circuits that require accurate knowledge of generator internal mechanical and electrical characteristics and idealization of the input vibration source, which cannot be assumed in general application. Variations in source vibration and load resistance are explored for a commercially available piezoelectric generator. The results agree with numerical and theoretical predictions in the previous literature for optimal power harvesting in sinusoidal and flat broadband vibration scenarios. Going beyond idealized steady-state sinusoidal and flat random vibration input, experimental SOR testing allows for more accurate representation of real world ambient vibration. It is shown that characteristic interactions from more complex vibration sources significantly alter power generation and processing requirements by varying harvested power, shifting optimal conditioning impedance, inducing voltage fluctuations, and ultimately rendering idealized sinusoidal and random analyses incorrect.
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4

vom Scheidt, J., and U. Wöhrl. "Nonlinear Vibration Systems with Two Parallel Random Excitations." Zeitschrift für Analysis und ihre Anwendungen 16, no. 1 (1997): 217–28. http://dx.doi.org/10.4171/zaa/760.

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5

Tabandeh, Armin, and Paolo Gardoni. "Nonlinear random vibration analysis: A Bayesian nonparametric approach." Probabilistic Engineering Mechanics 66 (October 2021): 103163. http://dx.doi.org/10.1016/j.probengmech.2021.103163.

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6

Roy, R. V., and P. D. Spanos. "Padé-type approach to nonlinear random vibration analysis." Probabilistic Engineering Mechanics 6, no. 3-4 (September 1991): 119–28. http://dx.doi.org/10.1016/0266-8920(91)90002-l.

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7

Krenk, S., and J. B. Roberts. "Local Similarity in Nonlinear Random Vibration." Journal of Applied Mechanics 66, no. 1 (March 1, 1999): 225–35. http://dx.doi.org/10.1115/1.2789151.

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A response analysis procedure is developed for oscillators with highly nonlinear stiffness and light nonlinear damping excited by non-white wide-band random noise based on local similarity between the random response and the deterministic response at the same energy level of the corresponding undamped oscillator. The analysis consists of three parts: introduction of modified phase plane variables, derivation of an approximate general form of the probability density of the response energy. for non-white excitation, and derivation of the spectral density function of the response from the conditional covariance function for a given energy level. The use of modified phase plane variables leads to a completely symmetric formulation and reformulates the stiffness nonlinearity as a nonlinear variation of the instantaneous angular frequency, and thereby a local rescaling of time. The probability density is obtained by averaging the full Fokker-Plank-Kolmogorov equation using local similarity, thus avoiding some theoretical problems associated with the traditional averaging of the stochastic differential equations. The use of local similarity with the exact undamped solution in the derivation of the conditional spectral density leads to a spectral density estimate, that contains the higher harmonic components explicitly. Comparisons of theoretical predictions with digital simulation estimates of both the probability and spectral densities for the Duffing oscillator demonstrate the accuracy of the theory.
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8

Wu, Penghui, Yan Zhao, and Xianghong Xu. "Power spectral density analysis for nonlinear systems based on Volterra series." Applied Mathematics and Mechanics 42, no. 12 (November 24, 2021): 1743–58. http://dx.doi.org/10.1007/s10483-021-2794-7.

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AbstractA consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.
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9

Igusa, T., and R. Sinha. "Response Analysis of Secondary Systems With Nonlinear Supports." Journal of Pressure Vessel Technology 113, no. 4 (November 1, 1991): 524–31. http://dx.doi.org/10.1115/1.2928790.

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This paper introduces a simplified random vibrations analysis method of linear secondary systems with nonlinear supports. The method separates, as much as possible, the nonlinear analysis of the supports from the linear analysis of the remainder of the secondary system. Equivalent linearization is used to generate response-dependent linear properties of the supports directly from hysteresis loops. These properties are then combined with the properties of the secondary system, and a response analysis is performed using mode combination. The analysis procedure is simpler than standard random vibration methods, and for narrow-band responses, it accurately models nonlinear behavior. In addition, the procedure uses equivalent modal quantities, such as natural frequencies and damping ratios, which provide insight into the effects of the nonlinear supports on the secondary system.
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10

Shintani, Masanori, and Manabu Hamai. "Study on Analytical Model of Nonlinear Vibration for Elastic Plates With Gaps Under Random Waves." Journal of Pressure Vessel Technology 126, no. 4 (November 1, 2004): 504–9. http://dx.doi.org/10.1115/1.1689359.

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In this paper, an analytical model for the nonlinear elastic-plastic vibration for long plates with gaps subjected to random vibrations is considered. The nonlinear vibration is caused by the collision phenomena between a mass through a gap and plates with thickness of 0.5, 0.6, and 0.8 mm. An elastic perfectly plastic solid material is assumed in some cases, which adds another aspect to the nonlinear behavior of the system. The material characteristic of the steel is assumed to be an elasto-plasticity solid model. A restoring force characteristic is obtained as the nonlinear vibration of a cubic equation for 0.5, 0.6, and 0.8 mm, the thickness of the plates by experiments. Now the analytical model is proposed by the elasto-plasticity solid model. The relation between the displacement and the force is described by a complicated equation. The curve from the analytical model is called a deflection curve. The results by the analytical model are compared with the results by the experimental model. The restoring force characteristics by the analysis agree with those of the experiment. The restoring force characteristics of the analysis are described using cubic equations. The simple analysis model for evaluation of the vibration characteristic of the nonlinear vibration system, which performs collision vibration with gaps, is proposed by elasto-plasticity solid model in this paper. The results of this proposed analytical model agree with the experimental results better than the results of the minimum of error of square.
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11

Ghanem, R., and P. D. Spanos. "A stochastic Galerkin expansion for nonlinear random vibration analysis." Probabilistic Engineering Mechanics 8, no. 3-4 (January 1993): 255–64. http://dx.doi.org/10.1016/0266-8920(93)90019-r.

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12

Barraza-Contreras, Jesús M., Manuel R. Piña-Monarrez, Alejandro Molina, and Roberto C. Torres-Villaseñor. "Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model." Applied Sciences 12, no. 9 (April 24, 2022): 4310. http://dx.doi.org/10.3390/app12094310.

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The paper’s content allowed us to determine the fatigue life of a component that is being subjected to a random vibration environment. Its estimation is performed in the frequency domain with loading frequencies being closer to the system’s natural frequency. From loads’ amplitude and their interaction effect, we derive a nonlinear damage model to cumulate the generated fatigue damage. The exponent value of 0.4 from the Manson–Halford curve damage model was replaced by a vibration bending stress relation that considers the effect and interaction of loads. The analysis is performed from a progressive accelerated vibration spectrum to predict the fatigue life estimation. From this accelerated scenario, the accelerated coefficients and cumulated damage are both determined. The proposed nonlinear model is based on the following facts: (1) vibration and bending stress σvb values are obtained from the response acceleration of power spectral density (PSD) applied and (2) the model can be applied to any mechanical component analysis where the corresponding acceleration responses Ares and the dynamic load factor σdynamic values are known. The steps to determine the expected fatigue damage accumulation D by using the curve damage are given.
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13

Barraza-Contreras, Jesús M., Manuel R. Piña-Monarrez, Alejandro Molina, and Roberto C. Torres-Villaseñor. "Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model." Applied Sciences 12, no. 9 (April 24, 2022): 4310. http://dx.doi.org/10.3390/app12094310.

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The paper’s content allowed us to determine the fatigue life of a component that is being subjected to a random vibration environment. Its estimation is performed in the frequency domain with loading frequencies being closer to the system’s natural frequency. From loads’ amplitude and their interaction effect, we derive a nonlinear damage model to cumulate the generated fatigue damage. The exponent value of 0.4 from the Manson–Halford curve damage model was replaced by a vibration bending stress relation that considers the effect and interaction of loads. The analysis is performed from a progressive accelerated vibration spectrum to predict the fatigue life estimation. From this accelerated scenario, the accelerated coefficients and cumulated damage are both determined. The proposed nonlinear model is based on the following facts: (1) vibration and bending stress σvb values are obtained from the response acceleration of power spectral density (PSD) applied and (2) the model can be applied to any mechanical component analysis where the corresponding acceleration responses Ares and the dynamic load factor σdynamic values are known. The steps to determine the expected fatigue damage accumulation D by using the curve damage are given.
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14

You, Feng Xiang, Fei Zhang, and Buo Lei Zuo. "Random Response Analysis for Nonlinear Systems of Composite Laminates." Advanced Materials Research 415-417 (December 2011): 56–61. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.56.

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Geometric parameters of composite materials often have a random nature in engineering structures. How to study random response and statistical properties of nonlinear systems with random parameters has a very important significance for reliability and optimization of structural design. In this paper, perturbation method and random central difference method are explored to establish composite nonlinear vibration equations and computational model to study random responses of nonlinear systems with random parameters under deterministic loading of the composite laminates, numerical examples illustrate the correctness of the algorithm.
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15

Guo, Yongbo, Dekun Zhang, Xinyue Zhang, Songquan Wang, and Wan Ma. "Experimental Study on the Nonlinear Dynamic Characteristics of Wire Rope under Periodic Excitation in a Friction Hoist." Shock and Vibration 2020 (February 17, 2020): 1–14. http://dx.doi.org/10.1155/2020/8506016.

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The nonlinear dynamic responses of a wire rope under periodic excitation in a friction hoisting system are investigated. Longitudinal excitation experiments of different periodic excitation frequencies are performed. The nonlinear dynamic characteristics of the rope, including transverse, longitudinal, and coupled vibrations, are discussed with time-frequency analysis. The results show that the transverse vibration is a forced vibration following the excitation, while the longitudinal vibration shows a complex, random vibration state. The vibration amplitude and intensity deviate significantly from their linear trend (superharmonic resonance) at some excitation frequencies, and this deviation indicates the typical nonlinear multiorder natural frequency characteristics. The lifting motion can lead to additional corrugated high-order harmonics and cause a fundamental wave distortion of low-frequency excitation. Experimental evidence for the coupling characteristics of the transverse-longitudinal rope vibration in the lifting process is found.
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16

Moon, F. C. "Nonlinear Dynamical Systems." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1284–86. http://dx.doi.org/10.1115/1.3143693.

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New discoveries have been made recently about the nature of complex motions in nonlinear dynamics. These new concepts are changing many of the ideas about dynamical systems in physics and in particular fluid and solid mechanics. One new phenomenon is the apparently random or chaotic output of deterministic systems with no random inputs. Another is the sensitivity of the long time dynamic history of many systems to initial starting conditions even when the motion is not chaotic. New mathematical ideas to describe this phenomenon are entering the field of nonlinear vibrations and include ideas from topology and analysis such as Poincare´ maps, fractal dimensions, Cantor sets and strange attractors. These new ideas are already making their way into the engineering vibrations laboratory. Further research in this field is needed to extend these new ideas to multi-degree of freedom and continuum vibration problems. Also the loss of predictability in certain nonlinear problems should be studied for its impact on the field of numerical simulation in mechanics of nonlinear materials and structures.
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17

Tong, Cao, Xiaoyuan Liu, and Li Fan. "Study on Nonlinear Vibration Analysis of Gear System with Random Parameters." IOP Conference Series: Earth and Environmental Science 128 (March 2018): 012100. http://dx.doi.org/10.1088/1755-1315/128/1/012100.

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18

Chang, T. P., H. C. Chang, and M. F. Liu. "A finite element analysis on random vibration of nonlinear shell structures." Journal of Sound and Vibration 291, no. 1-2 (March 2006): 240–57. http://dx.doi.org/10.1016/j.jsv.2005.06.004.

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19

Khiem, Nguyen Tien. "Spectral analysis of vibration in weakly non-linear systems." Vietnam Journal of Mechanics 22, no. 3 (September 30, 2000): 181–92. http://dx.doi.org/10.15625/0866-7136/9974.

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The weakly nonlinear systems subjected to deterministic excitations have been fully and deeply studied by use of the well developed asymptotic methods [1-4]. The systems excited by a random load have been investigated mostly using the Fokker-Plank-Kolmogorov equation technique combined with the asymptotic methods [5-8]. However, the last approach in most successful cases allows to obtain only a stationary single point probability density function, that contains no information about the correlation nor' consequently, the spectral structure of the response. The linearization technique [9, 10] in general permits the spectral density of the response to be determined, but the spectral function obtained by this method because of the linearization eliminates the effect of the nonlinearity. Thus, spectral structure of response of weakly nonlinear systems to random excitation, to the author's knowledge, has not been studied enough. This paper deals with the above mentioned problem. The main idea of this work is the use of an analytical simulation of random excitation given by its spectral density function and afterward application of the well known procedure of the asymptotic method to obtain an asymptotic expression of the response spectral density function. The obtained spectral relationship covers the linear system case and especially emphasizes the nonlinear effect on the spectral density of response. The theory will be illustrated by an example and at the end of this paper there will be a discussion about the obtained results.
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20

Zhou, Shihua, Guiqiu Song, Mengnan Sun, and Zhaohui Ren. "Nonlinear dynamic response analysis on gear-rotor-bearing transmission system." Journal of Vibration and Control 24, no. 9 (August 30, 2016): 1632–51. http://dx.doi.org/10.1177/1077546316667178.

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A coupled lateral-torsional nonlinear dynamic model with 16-degree-of-freedom (16-DOF) of gear-rotor-bearing transmission system (GRBTS) is developed after comprehensive considering the nonlinear features associated with time-varying meshing stiffness, backlash, transmission error, friction force, input/output load, gravity and gear eccentricity. Based on the nonlinear differential equations, the coupled multi-body dynamic responses of the GRBTS are demonstrated using the Runge-Kutta numerical method, and the effects of friction coefficient and mean load on the dynamic characteristics are investigated. The results show that the friction force could enlarge the vibration amplitude and affect the low frequency components seriously. The mean load excitation has a complicated influence on the coupled GRBTS, and the torsional vibration is the dominate response. Whereas the mean load excitation has a certain extent vibration suppression, and light load and heavy load could no longer effectively control the nonlinear vibration of the GRBTS. With the increasing of rotational speed, the friction coefficient and mean load ranges of the chaotic behavior widen and the chaotic characteristics strengthens. It is shown that small parameter random perturbation might be propagated in the vibration system and lead to relatively large vibration of the system. The contribution to provide a reference for the design and study of gear system.
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21

Chaudhari, Virendra Kumar, Niranjan L. Shegokar, and Achchhe Lal. "Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework." Curved and Layered Structures 4, no. 1 (January 26, 2017): 85–103. http://dx.doi.org/10.1515/cls-2017-0007.

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AbstractThis paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC) beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT) with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT),Second order perturbation technique (SOPT) and Monte Carlo simulation (MCS) methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV) and probability density function (PDF) for various aforementioned parameters.
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22

Hao, Ying, Ming Gao, and Jiajie Gong. "Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation." Materials 15, no. 2 (January 12, 2022): 562. http://dx.doi.org/10.3390/ma15020562.

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The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.
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23

Baber, Thomas T., and Mohammed N. Noori. "Modeling General Hysteresis Behavior and Random Vibration Application." Journal of Vibration and Acoustics 108, no. 4 (October 1, 1986): 411–20. http://dx.doi.org/10.1115/1.3269364.

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A simple constructive technique for the development of rate-type hysteresis models for general nonlinear system is presented. The technique is used to develop hysteresis models to incorporate time history-dependent postyield restorting forces, and general pinching behavior in smoothly varying deteriorating models. Applications of these models to random vibration analysis modeling via simulation and equivalent linearization techniques under Gaussian noise excitation is presented.
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24

Rassaian, Mostafa. "Power Spectral Density Conversions and Nonlinear Dynamics." Shock and Vibration 1, no. 4 (1994): 349–56. http://dx.doi.org/10.1155/1994/903103.

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To predict the vibration environment of a payload carried by a ground or air transporter, mathematical models are required from which a transfer function to a prescribed input can be calculated. For sensitive payloads these models typically include linear shock isolation system stiffness and damping elements relying on the assumption that the isolation system has a predetermined characteristic frequency and damping ratio independent of excitation magnitude. In order to achieve a practical spectral analysis method, the nonlinear system has to be linearized when the input transportation and handling vibration environment is in the form of an acceleration power spectral density. Test data from commercial isolators show that when nonlinear stiffness and damping effects exist the level of vibration input causes a variation in isolator resonant frequency. This phenomenon, described by the stationary response of the Duffing oscillator to narrow-band Gaussian random excitation, requires an alternative approach for calculation of power spectral density acceleration response at a shock isolated payload under random vibration. This article details the development of a plausible alternative approach for analyzing the spectral response of a nonlinear system subject to random Gaussian excitations.
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25

Hua, CR, Y. Zhao, ZW Lu, and H. Ouyang. "Random vibration of vehicle with hysteretic nonlinear suspension under road roughness excitation." Advances in Mechanical Engineering 10, no. 1 (January 2018): 168781401775122. http://dx.doi.org/10.1177/1687814017751222.

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The analysis of random vibration of a vehicle with hysteretic nonlinear suspension under road roughness excitation is a fundamental part of evaluation of a vehicle’s dynamic features and design of its active suspension system. The effective analysis method of random vibration of a vehicle with hysteretic suspension springs is presented based on the pseudoexcitation method and the equivalent linearisation technique. A stable and efficient iteration scheme is constructed to obtain the equivalent linearised system of the original nonlinear vehicle system. The power spectral density of the vehicle responses (vertical body acceleration, suspension working space and dynamic tyre load) at different speeds and with different nonlinear levels of hysteretic suspension springs are analysed, respectively, by the proposed method. It is concluded that hysteretic nonlinear suspensions influence the vehicle dynamic characteristic significantly; the frequency-weighted root mean square values at the front and rear suspensions and the vehicle’s centre of gravity are reduced greatly with increasing the nonlinear levels of hysteretic suspension springs, resulting in better ride comfort of the vehicle.
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26

Huang, Dongmei, Shengxi Zhou, Qun Han, and Grzegorz Litak. "Response analysis of the nonlinear vibration energy harvester with an uncertain parameter." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 2 (December 4, 2019): 393–407. http://dx.doi.org/10.1177/1464419319893211.

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In this paper, the Chebyshev polynomial approximation is firstly utilized to analyze the dynamical characteristics of the nonlinear vibration energy harvester with an uncertain parameter. First, the stochastic energy harvester is transformed into a high-dimensional equivalent deterministic system by the Chebyshev polynomial approximation. And the ensemble mean response of the stochastic energy harvester is introduced to discuss the stochastic response. Then, the effectiveness of the approximation method is verified by numerical results. Furthermore, the bifurcation property of the displacement and voltage is analyzed, which is also consistent with the results derived by the top Lyapunov exponent. It is found that random factor can induce the appearance of multi-periodic phenomena and lead to appear the behavior of the periodic bifurcation. The strong random factor induces the fluctuation of the output voltage. In addition, the existence of the random factor greatly influences the property of the sub-harmonics and super-harmonics of the spectrum. Overall, the response mechanism of the nonlinear vibration energy harvester with an uncertain parameter is revealed.
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27

Wang, Rubin, Yun-Bo Duan, and Zhikang Zhang. "Resonance analysis of the finite-damping nonlinear vibration system under random disturbances." European Journal of Mechanics - A/Solids 21, no. 6 (November 2002): 1083–88. http://dx.doi.org/10.1016/s0997-7538(02)01237-8.

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28

Karimi, A. H., and M. Shadmani. "Nonlinear vibration analysis of a beam subjected to a random axial force." Archive of Applied Mechanics 89, no. 2 (October 29, 2018): 385–402. http://dx.doi.org/10.1007/s00419-018-1474-7.

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29

Wen, Y. K. "Methods of Random Vibration for Inelastic Structures." Applied Mechanics Reviews 42, no. 2 (February 1, 1989): 39–52. http://dx.doi.org/10.1115/1.3152420.

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Structures often become nonlinear and inelastic under severe lateral force produced by natural hazards such as earthquakes, severe winds and waves. The restoring force of the structures under such load may become hysteretic and deteriorate in strength or stiffness, or both. This paper gives an overview of the major developments in the modeling and response analysis of inelastic structures under random excitation. It includes: (1) modeling of the hereditary behavior of inelastic system; (2) methods of solution based on semi-empirical approaches, Fokker–Planck equation, and equivalent linearization; and (3) applications to performance and safety evaluation of real structural systems. Limitations of current methods are mentioned and suggestions of areas for further research are given.
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30

Li, Dong, Zhou-Lian Zheng, Rui Yang, and Peng Zhang. "Analytical Solutions for Stochastic Vibration of Orthotropic Membrane under Random Impact Load." Materials 11, no. 7 (July 18, 2018): 1231. http://dx.doi.org/10.3390/ma11071231.

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Orthotropic membrane materials have been applied in the numerous fields, such as civil engineering, space and aeronautics, and mechanical engineering, among others. During their serving lifespan, these membranes are always facing strong stochastic vibrations induced by the random impact load such as hail, heavy rain, and noise, among others. In this paper, the stochastic vibration problem of orthotropic membrane subjected to random impact load is investigated. The statistical characteristics of random impact load are initially obtained based on the stochastic pulse theory. Then, the Von Karman theory is applied to model the nonlinear vibration of membrane with geometric nonlinearity, which is then used to derive and solve the corresponding fokker–plank–kolmogorov (FPK). The theoretical model developed is validated by means of experiment study and monte carlo simulation (MCS) analysis. The effects of variables like pretension force, velocity of impact load, and material features on stochastic dynamic behavior of membranes are discussed in detail. This exposition provides theoretical framework for stochastic vibration control and design of membranes subjected to random dynamic load.
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31

Yang, Zheng, Buyu Jia, Quansheng Yan, Xiaolin Yu, and Yinghao Zhao. "Nonlinear Stochastic Analysis of Footbridge Lateral Vibration Based on Probability Density Evolution Method." Shock and Vibration 2019 (October 27, 2019): 1–16. http://dx.doi.org/10.1155/2019/2606395.

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Footbridge lateral vibration remains an unsolved problem and is characterized by the following: (1) pedestrians are sensitive to bridge vibration, which causes the pedestrian’s excitation being dependent on the bridge vibration; (2) pedestrian lateral excitation is a stochastic process rather than a perfect periodic load. Therefore, footbridge lateral vibration is essentially a complex nonlinear stochastic vibration system. Thus far, an effective method of dealing with such nonlinear stochastic vibration of footbridges remains lacking. A framework based on the probability density evolution (PDE) method is presented. For the mathematical model, the parameter resonance model is used to describe the pedestrian-bridge interaction while treating the pedestrian lateral excitation as a narrow-band process. For the analysis method, PDE is used to solve the nonlinear stochastic equations in combination with the number theoretical and finite difference methods. The proposed method establishes a new approach in studying footbridge lateral vibration. First, PDE based on the small sample strategy avoids the large amount of computation. Second, the randomness of both structural parameters and pedestrian lateral excitation could be taken into consideration by the proposed method. Third, based on the probability results with rich information, the serviceability, dynamic reliability, and random stability analyses are realized in a convenient manner.
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32

Wu, Sean F., and Jinshuo Zhu. "Stability Analysis of a Nonlinear Plate in Mean Flow." Journal of Computational Acoustics 05, no. 02 (June 1997): 137–55. http://dx.doi.org/10.1142/s0218396x97000095.

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A stability analysis of a nonlinear plate clamped to an infinite baffle in mean flow is given. The effect of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion, and that of viscous damping are taken into account in the derivation of the plate equation. The plate flexural displacement is obtained by modal expansion based on Galerkin's method. The critical mean flow speeds at which local instabilities may occur are determined by Routh algorithm. The mechanisms that trigger the local instabilities are uncovered. The effect of structural nonlinearities, and that of plate aspect and plate length/thickness ratios on local instabilities are examined. Numerical examples of the transition from stable to locally unstable vibration, as the mean flow speed exceeds the critical values, are demonstrated. The results show that while the overall amplitude of the plate flexural displacement may be bounded when the mean flow speed exceeds the critical values, plate vibration may be locally unstable, jumping from one equilibrium position to another. Furthermore, the jumping may be random, and the plate vibration may seem chaotic. The results also show that viscous damping may stabilize plate flexural vibration and settle the plate in one of its equilibria.
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33

Ren, Dongdong, Yangwu Yao, Huiyuan Wang, Huixian Qu, and Guoqiang Wang. "Nonlinear Dynamic Response Analysis of a Three-Stage Gear Train Based on Lightweight Calculation for Edge Equipment." Computational Intelligence and Neuroscience 2022 (August 21, 2022): 1–8. http://dx.doi.org/10.1155/2022/4724504.

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Bevel gears are widely used in aerospace transmission systems as well as modern mechanical equipment. In order to meet the needs and development of aerospace, high-speed dynamic vehicles, and various defense special equipment, higher and higher requirements are made for the high precision and stability of gear transmission systems, as well as the prediction and control of noise and vibration. Considering the nonlinear factors such as comprehensive gear error and tooth side clearance, a dynamic model of the three-stage gear transmission system is established. The relevant physical parameters, geometric parameters, and load parameters in the gear system are considered random variables to obtain the stochastic vibration model. When the random part of the random parameters is much smaller than the deterministic part, the vibration differential equation is expanded into a first-order term at the mean of the random parameter vector according to the Taylor series expansion theorem, and the ordering equation is solved numerically. Based on the improved stochastic regression method, the nonlinear dynamic response analysis of the three-stage gear train is carried out. This results in a relatively stable system when the dimensionless excitation frequency is in the range of 0.716 to 0.86 and the magnitude of the dimensionless integral meshing error is < 1.089.
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34

Leng, Dingxin, Haiyan Xiao, Lei Sun, Guijie Liu, Xiaojie Wang, and Lingyu Sun. "Study on a magnetorheological elastomer-base device for offshore platform vibration control." Journal of Intelligent Material Systems and Structures 30, no. 2 (November 14, 2018): 243–55. http://dx.doi.org/10.1177/1045389x18808398.

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Wave loading is one of the leading factors contributing to fatigue damage of offshore platforms. Vibrations in marine platforms due to nonlinear hydrodynamic forces can reduce platform productivity, endanger safety, and affect serviceability. This article presents numerical evaluation of a magnetorheological elastomer device for wave-induced vibration reduction of offshore platform. Random wave loadings are estimated by wave spectrum analysis and Morison’s equations. By altering field-induced stiffness of magnetorheological elastomers and non-resonance control strategy, the wave-induced vibration of offshore platform is effectively reduced, and the magnetorheological elastomer device presents strong control robustness under various wave loadings. This work indicates that magnetorheological elastomer-base device may open a new insight for vibration mitigation of ocean structures.
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35

Yan-li, He, Ma Xing, and Wang Zhao-min. "Nonlinear discrete analysis method for random vibration of guyed masts under wind load." Journal of Wind Engineering and Industrial Aerodynamics 91, no. 4 (March 2003): 513–25. http://dx.doi.org/10.1016/s0167-6105(02)00451-8.

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36

Fei-Yue, Wang. "Monte Carlo analysis of nonlinear vibration of rectangular plates with random geometric imperfections." International Journal of Solids and Structures 26, no. 1 (1990): 99–109. http://dx.doi.org/10.1016/0020-7683(90)90097-f.

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37

Wang, Ziqi, and Junho Song. "Equivalent linearization method using Gaussian mixture (GM-ELM) for nonlinear random vibration analysis." Structural Safety 64 (January 2017): 9–19. http://dx.doi.org/10.1016/j.strusafe.2016.08.005.

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38

MATSUMOTO, Hiroyuki, Shinji YAMAKAWA, and Hisami OHISHI. "Spectral Analysis and Identification of Nonlinear Vibration System Subjected to a Random Input." Transactions of the Japan Society of Mechanical Engineers Series C 62, no. 604 (1996): 4491–98. http://dx.doi.org/10.1299/kikaic.62.4491.

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39

Chandrashekhar, M., and Ranjan Ganguli. "Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties." International Journal of Mechanical Sciences 52, no. 7 (July 2010): 874–91. http://dx.doi.org/10.1016/j.ijmecsci.2010.03.002.

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40

Lin, Wei, Cheng Su, and Youhong Tang. "Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads." Journal of Marine Science and Engineering 8, no. 12 (December 8, 2020): 1001. http://dx.doi.org/10.3390/jmse8121001.

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This paper is devoted to the random vibration analysis of jacket platforms under wave loads using the explicit time-domain approach. The Morison equation is first used to obtain the nonlinear random wave loads, which are discretized into random loading vectors at a series of time instants. The Newmark-β integration scheme is then employed to construct the explicit expressions for dynamic responses of jacket platforms in terms of the random vectors at different time instants. On this basis, Monte Carlo simulation can further be conducted at high efficiency, which not only provides the statistical moments of the random responses, but also gives the mean peak values of responses. Compared with the traditional power spectrum method, nonlinear wave loads can be readily taken into consideration in the present approach rather than using the equivalent linearized Morison equation. Compared with the traditional Monte Carlo simulation, the response statistics can be obtained through the direct use of the explicit expressions of dynamic responses rather than repeatedly solving the equation of motion. An engineering example is analyzed to illustrate the accuracy and efficiency of the present approach.
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41

Zhao, Qiu Fang, Man Dun Jiao, and Jian Qiang Xing. "Application of Virtual Prototyping Technology in the Design of Drive Axle." Applied Mechanics and Materials 127 (October 2011): 252–56. http://dx.doi.org/10.4028/www.scientific.net/amm.127.252.

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In this paper, a virtual prototype model of the nonlinear vibration system is built by using the ADAMS(Automatic Dynamic Analysis of Mechanical Systems), and the simulation process of the hydro-pneumatic suspension is presented. A simulation analysis of the drive axle is done with road unevenness. The result shows that it is more important to consider the nonlinear damping than the nonlinear stiffness in the analysis of a nonlinear structure with a random response sometimes.
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42

Liu, Jie, and Chao Feng Li. "Research on the Annoyance Rate of Vehicle Vibration Serviceability." Applied Mechanics and Materials 291-294 (February 2013): 2738–43. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.2738.

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An important problem in current analysis method is that one can hardly know the exact structural design effects when using the conventional guidelines. In order to solve the problem, the annoyance rate analytical method suitable for vibration serviceability analysis of vehicle was constructed from a viewpoint of psychophysics, based on the existing basic method of methods and referenced to experimental studies at home and abroad. As an application example of annoyance rate method, a nonlinear vibrations system with two-DOF was built. The acceleration response of the vibration system under random loads of Gaussian distribution was analyzed with the new method. The result shows that the most important advantage of the annoyance-rate method is that it has the more quantitative characteristic and its results well coincide with those of the ISO method.
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43

Bucher, C. G. "Approximate Nonstationary Random Vibration Analysis for MDOF Systems." Journal of Applied Mechanics 55, no. 1 (March 1, 1988): 197–200. http://dx.doi.org/10.1115/1.3173629.

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An approximate method for nonstationary random vibration analysis is presented. This method utilizes properties of the stationary solution for simplifying the analysis. This approach has previously been applied by the author to linear and nonlinearly damped SDOF systems. In the present paper the concept is extended to linear MDOF systems and applied to nonstationary earthquake-type loading. Comparisons with available exact solutions show very good agreement in numerical results with the additional benefit of reducing computer time by more than one order of magnitude.
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44

Kim, Yeong-Nam, Jae-Sang Park, Eun-Soo Go, Min-Hyuk Jeon, and In-Gul Kim. "Nonlinear Random Response Analyses of Panels Considering Transverse Shear Deformations under Combined Thermal and Acoustic Loads." Shock and Vibration 2018 (June 20, 2018): 1–11. http://dx.doi.org/10.1155/2018/9751038.

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The panel structures of flight vehicles at supersonic or hypersonic speeds are subjected to combined thermal, acoustic, and aerodynamic loads. Because of the combined thermal and acoustic loads, the panel structure may exhibit nonlinear random vibration responses, such as the snap-through phenomenon and random vibrations. These unique dynamic behaviors of the panel structure under combined thermal and acoustic loads can result in serious damage or fatigue failure of the panel structures of high-speed flight vehicles. This study investigates the nonlinear random responses of thin and thick panels under combined thermal and acoustic loads. The panels are modeled based on the first-order shear deformation theory (FSDT) to account for transverse shear deformations. The von-Karman nonlinear strain–displacement relationship is used for geometric nonlinearity in the out-of-plane direction of the panel. The thermal load distribution is assumed to be constant in the thickness direction of the panel. The random acoustic load is represented as stationary White–Gaussian random pressure with zero mean and uniform magnitude over the panels. Static and dynamic equations are derived using the principle of virtual work and the nonlinear finite element method. A thermal postbuckling analysis is conducted using the Newton–Raphson method, and the dynamic nonlinear equations are solved using the Newmark-β time integration method. In the present numerical analyses, the snap-through responses for both the thin and thick panels are investigated, and the results indicate that the loading conditions that cause snap-through are different for thin and thick panels.
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45

Shegokar, Niranjan L., and Achchhe Lal. "Stochastic Nonlinear Free Vibration Analysis of Functionally Graded Beam Subjected to Thermal Loading with Random Material Properties." Advanced Materials Research 747 (August 2013): 551–54. http://dx.doi.org/10.4028/www.scientific.net/amr.747.551.

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This paper deals with the stochastic nonlinear free vibration response of functionally graded materials (FGMs) beam subjected to thermal loadings with uncertain material properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituents material and volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C0 continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) is used for FGMs beam to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with the results available in literatures and independent Monte Carlo simulation (MCS).
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46

Lal, Achchhe, and Niranjan L. Shegokar. "Thermoelectrically induced nonlinear free vibration analysis of piezo laminated composite conical shell panel with random fiber orientation." Curved and Layered Structures 4, no. 1 (September 26, 2017): 237–54. http://dx.doi.org/10.1515/cls-2017-0016.

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Abstract This paper presents the free vibration response of piezo laminated composite geometrically nonlinear conical shell panel subjected to a thermo-electrical loading. The temperature field is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E2 only. The material properties are assumed to be independent of the temperature and the electric field. The basic formulation is based on higher order shear deformation plate theory (HSDT) with von-Karman nonlinearity. A C0 nonlinear finite element method based on direct iterative approach is outlined and applied to solve nonlinear generalized eigenvalue problem. Parametric studies are carried out to examine the effect of amplitude ratios, stacking sequences, cone angles, piezoelectric layers, applied voltages, circumferential length to thickness ratios, change in temperatures and support boundary conditions on the nonlinear natural frequency of laminated conical shell panels. The present outlined approach has been validated with those available results in the literature.
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47

Chernyak, Mykola, and Markiyan Lesyuk. "Mathematical model of instrumental vibration error of angular velocity sensor." MECHANICS OF GYROSCOPIC SYSTEMS, no. 42 (December 28, 2022): 5–13. http://dx.doi.org/10.20535/0203-3771422021268457.

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The problem of mathematical description of the influence of harmful deterministic and broadband random vibrations of a moving object on the measurement result of the sensor of the angular velocity of rotation of this object installed on it is considered. It is shown that under such conditions a systematic instrumental vibration error arises in the angular velocity sensor. The source of this error is the nonlinearity of the static conversion function of the angular velocity sensor and the asymmetry of its conversion coefficient. A mathematical model of this error has been obtained. Formulas for calculating the vibrational error of the angular velocity sensor are obtained depending on the apparent angular velocity of the flight of the aircraft, the vibration parameters of the base on which the sensor is installed and the parameters of the nonlinear sensor conversion function. This model makes it possible to calculate the value of the vibration error under specified vibration conditions for a specific angular velocity sensor (direct analysis problem), as well as to select an angular velocity sensor based on the values ​​of its conversion function coefficients, based on ensuring the required accuracy of measuring the angular velocity of a moving object using this angular velocity sensor (inverse synthesis problem).
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48

Zhang, Zhange, Wenbo Ji, Bowen Yang, Junzhou Huo, and Xuanxuan Li. "Dynamic analysis and vibration reduction of mechanical-hydraulic coupled tunnel boring machine (TBM) main drive system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 1 (October 1, 2021): 115–25. http://dx.doi.org/10.1177/09544062211029330.

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Tunnel Boring Machine always works in the changeable geologies with multiple drivers, which leads to severe vibration of the TBM main drive system and key component failures. The vibration characteristics of TBM under different working conditions and the vibration reduction analysis have important meanings. First of all, by considering the time-varying random loads of the cutters, the contact force of the gears, the stiffness of the main bearing, and the stiffness of the cylinders, a mechanical-hydraulic coupling nonlinear dynamic model of the TBM main drive system was built according to the assembly relationship and load transmission path of the main drive system. Secondly, the dynamic model of the TBM main drive system is verified by comparing the theoretical vibration with the real vibration of the TBM main drive system. The error of the vibration acceleration is 10% to 30%. Three typical loads are defined under typical working conditions, and the vibrations of the TBM main drive system under three typical loads were analyzed. Finally, the sensitivity analysis of the cylinder damping shows that the damping at the position of the propulsion cylinder has a great influence on the vibration of the TBM main drive system. The results show that when the damping coefficient is 2.5 × 106 N·s/m, the maximum reduction of axial acceleration of cutterhead is 0.64 g, and that of the main beam front section is 0.55 g. The variable damping coefficient vibration reduction strategies under three typical loads are verified.
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49

Ibrahim, R. A. "Recent Results in Random Vibrations of Nonlinear Mechanical Systems." Journal of Mechanical Design 117, B (June 1, 1995): 222–33. http://dx.doi.org/10.1115/1.2836461.

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The influence of random vibration on the design of mechanical components has been considered within the framework of the linear theory of small oscillations. However, in some important cases this theory is inadequate and fails to predict some complex response characteristics that have been observed experimentally and which can only be predicted by nonlinear analyses. This paper describes some recent developments in the theory of nonlinear random vibration based on Markov methods and related problems in the design of dynamical systems. Research efforts have been focused on stability/bifurcation conditions, response statistics and reliability problems. Significant progress has been made in developing new analytical methods and conducting experimental testing. These developments have helped to resolve some controversies, and to enhance our understanding of difficult issues. Experimental and numerical simulations have revealed new phenomena that were not predicted analytically. These include on-off intermittency, snap-through phenomena, and the dependence of the response bandwidth on the excitation level. The main results of studying the responses of nonlinear single-and two-degree-of-freedom systems to random excitations obtained by the author and others are discussed in this paper.
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50

Ibrahim, R. A. "Recent Results in Random Vibrations of Nonlinear Mechanical Systems." Journal of Vibration and Acoustics 117, B (June 1, 1995): 222–33. http://dx.doi.org/10.1115/1.2838667.

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The influence of random vibration on the design of mechanical components has been considered within the framework of the linear theory of small oscillations. However, in some important cases this theory is inadequate and fails to predict some complex response characteristics that have been observed experimentally and which can only be predicted by nonlinear analyses. This paper describes some recent developments in the theory of nonlinear random vibration based on Markov methods and related problems in the design of dynamical systems. Research efforts have been focused on stability/bifurcation conditions, response statistics and reliability problems. Significant progress has been made in developing new analytical methods and conducting experimental testing. These developments have helped to resolve some controversies, and to enhance our understanding of difficult issues. Experimental and numerical simulations have revealed new phenomena that were not predicted analytically. These include on-off intermittency, snap-through phenomena, and the dependence of the response bandwidth on the excitation level. The main results of studying the responses of nonlinear single-and two-degree-of-freedom systems to random excitations obtained by the author and others are discussed in this paper.
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