Melnikov analysis of chaotic dynamics in an impact oscillator system

IF 3.2 3区工程技术 Q2 MECHANICS International Journal of Non-Linear Mechanics Pub Date : 2025-04-01 Epub Date: 2025-01-30 DOI:10.1016/j.ijnonlinmec.2025.105027

Yan Zhou , Peiyan Zhao , Yujie Guo

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Abstract

In this paper, the global dynamic characteristics of an impact oscillator in a class of complex non-smooth systems are discussed in depth by means of analytical and numerical analysis and the classical Melnikov theory. Firstly, the approximation method is used to obtain the fitting system, and the fitting system is compared with the original system. Subsequently, in order to further reveal the intrinsic chaos mechanism of the system, we apply the Melnikov method to determine the threshold conditions for the occurrence of homoclinic chaos in the system. Based on these threshold conditions, we systematically investigate the influence of key parameters such as recovery coefficient, excitation amplitude, excitation frequency and damping coefficient on the chaotic characteristics of the system. In particular, we analyze the transformation of system dynamics under different excitation amplitudes, and reveal the key role of excitation amplitude in regulating system stability. These research results provide new perspectives and tools for theoretical research in related fields, and also provide reference and guidance for the design and control of impact oscillators in practical engineering applications.

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冲击振子系统混沌动力学的Melnikov分析

本文采用解析和数值分析的方法，结合经典Melnikov理论，对一类复杂非光滑系统中冲击振子的全局动力学特性进行了深入的讨论。首先采用近似法得到拟合系统，并将拟合系统与原系统进行比较。随后，为了进一步揭示系统的内在混沌机制，我们应用Melnikov方法确定了系统发生同斜混沌的阈值条件。基于这些阈值条件，系统地研究了恢复系数、激励幅值、激励频率和阻尼系数等关键参数对系统混沌特性的影响。特别地，我们分析了不同激励幅值下系统动力学的变化，揭示了激励幅值在调节系统稳定性中的关键作用。这些研究成果为相关领域的理论研究提供了新的视角和工具，也为实际工程应用中的冲击振子设计与控制提供了参考和指导。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.