Parametric resonance and stochastic stability of a vibro-impact system under bounded noise excitation

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-01 Epub Date: 2025-02-19 DOI:10.1016/j.cnsns.2025.108715

Dongliang Hu , Jianfeng Zhang , Huatao Chen , Juan LG Guirao , Xianbin Liu

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Abstract

The vibro-impact system has more complex and variable dynamic behavior, and its research has attracted the attention of many scholars. However, the effect of resonance on the dynamic characteristics of vibro-impact systems is rarely explored. In this paper, the parametric resonance and stochastic stability of a vibro-impact system excited by bounded noise parameters are investigated. For weak noise excitations, the approximate analytical results of the moment Lyapunov exponent and the largest Lyapunov exponent are calculated by using the method of singular perturbation and Fourier series expansion, which are in good agreement with those obtained by Monte Carlo numerical simulation. Then, based on the moment Lyapunov exponent and the largest Lyapunov exponent, the effects of parametric resonance and different parameters on the stochastic stability of the vibro-impact system are investigated in detail.

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有界噪声激励下振动冲击系统的参数共振与随机稳定性

振动冲击系统具有较为复杂多变的动力行为，其研究受到了众多学者的关注。然而，共振对振动冲击系统动力特性的影响却很少被研究。研究了受有界噪声参数激励的振动冲击系统的参数共振和随机稳定性问题。在弱噪声激励下，用奇异摄动法和傅立叶级数展开法计算了矩Lyapunov指数和最大Lyapunov指数的近似解析结果，与蒙特卡罗数值模拟结果吻合较好。然后，基于矩Lyapunov指数和最大Lyapunov指数，详细研究了参数共振和不同参数对振冲系统随机稳定性的影响。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.