Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Chen, Lincong; Zhu, Haisheng; Sun, Jian‐Qiao

doi:10.1007/s10483-019-2543-5

Cited by 14 publications

(5 citation statements)

References 34 publications

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“…Such systems, referred to as vibroimpact systems, are typically described using differential equations with constraints due to the non-smooth nature of collisions and impacts [ 1 , 2 , 3 ]. This inherent non-smoothness introduces strong nonlinearity into the system dynamics, leading to complex behaviors and a high sensitivity to parameter changes [ 4 , 5 ]. Moreover, engineering structures are inevitably influenced by random factors such as air temperature variations, humidity changes, and ground vibrations [ 6 , 7 , 8 , 9 ].…”

Section: Introductionmentioning

confidence: 99%

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

Yang,

Deng,

et al. 2023

Entropy

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The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

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Section: Introductionmentioning

confidence: 99%

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

Yang,

Deng,

et al. 2023

Entropy

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“…Stochastic vibro-impact systems with two-sided barriers have more complicated factors, which have attracted extensive attention from scholars [14][15][16][17][18][19][20][21]. For examples, in a stochastic response study of vibro-impact system with bilateral barriers, the Ref.…”

Section: Introductionmentioning

confidence: 99%

“…For examples, in a stochastic response study of vibro-impact system with bilateral barriers, the Ref. [15] reported that an approximate transformation is employed to convert the vibro-impact system to a continuous form, then the closed-form stationary probability density function (PDF) is got by solving the reduced Fokker-Planck (FP) equation with the iterative method of weighted residue. And authors examined the accuracy of the proposed method by applying two typical single-degreeof-freedom (SDOF) vibro-impact systems with bilateral barriers under Gaussian white noise excitations.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

Ma¹,

Ning

Wang

et al. 2022

Preprint

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The research of stochastic steady-state response of vibration systems including bilateral impacts and gaps has important theoretical and practical significance. At present, conventional analytical methods destroy the inherent non-smooth of the systems because of many approximate transformations when solving response. In order to deal with this problem, we propose a new method to preserve the velocity jump under the bilateral impact without nonsmooth transformation in this paper. A complete process is regarded as the one-step transition probability that the stochastic trajectories start from one barrier, and return to the original barrier after impacting with another barrier. Then, the intervals of response are established based on the initial barrier to ensure of the continuity of the state space. We analyzed the steady-state response of a bilateral Rayleigh vibro-impact oscillator and a piezoelectric energy harvesting device with two symmetric barriers by utilizing the proposed method, respectively. Comparing with Monte Carlo simulations, it is fully demonstrated the effectiveness of this method. At the same time, it is found that the cases using our proposed method have wide applicability under different position of barriers, restitution coefficient, noise excitation and system parameters.

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“…Many studies show that the moment equivalence method can only guarantee integral equivalence, but improper results would be given in the prediction of power spectral density (PSD) [9] . Furthermore, the random average approach [10][11] , the Fokker-Planck-Kolmogorov (FPK) equation technique [12][13] , and the Wiener path integral approach [14][15] have been developed. In the field of practical application, the spectral analysis of nonlinear systems in the frequencydomain is very attractive.…”

Section: Introductionmentioning

confidence: 99%

Power spectral density analysis for nonlinear systems based on Volterra series

Zhao

2021

Appl. Math. Mech.-Engl. Ed.

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A 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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Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Cited by 14 publications

References 34 publications

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

Power spectral density analysis for nonlinear systems based on Volterra series

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