Nonlinear Vibration of a Multi-Degree-of-Freedom Gear Transmission System with Multi-Piecewise Linear Functions

IF 1.9 4区工程技术 Q3 ENGINEERING, MECHANICAL Journal of Computational and Nonlinear Dynamics Pub Date : 2023-02-07 DOI:10.1115/1.4056850

Fulin Liao, Jianliang Huang, Weidong Zhu

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Abstract

Periodic and period-doubling vibrations in a gear transmission system subjected to forced excitations with multi-piecewise linear functions are investigated in this work by using the incremental harmonic balance (IHB) method. The nonlinear ordinary differential equations that govern vibration of the gear transmission system are formulated by employing the Newton's second law. Analytical results reveal abundant interesting phenomena, including jumps, bifurcations, softening-spring behaviors, and primary, super-harmonic, and sub-harmonic resonances, which have not been exhibited in existing investigations on nonlinear vibrations of gear transmission systems. Nonlinear phenomena and resonances of the gear transmission system are revealed by considering different numbers of degrees of freedom of the system. The bifurcations containing saddle-node, period-doubling, and Hopf bifurcations are observed in frequency response curves. The period-doubling phenomena are characterized with phase-plane diagrams and Fourier spectra. Further, analytical results obtained by the IHB method match very well with those from numerical integration.

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多分段线性函数多自由度齿轮传动系统的非线性振动

本文采用增量谐波平衡(IHB)方法研究了受多分段线性函数强迫激励的齿轮传动系统的周期振动和倍周期振动。应用牛顿第二定律建立了控制齿轮传动系统振动的非线性常微分方程。分析结果揭示了许多有趣的现象，包括跳跃、分岔、软化弹簧行为以及初级、超谐波和次谐波共振，这些现象在现有的齿轮传动系统非线性振动研究中没有表现出来。考虑不同的自由度数，揭示了齿轮传动系统的非线性现象和共振现象。频率响应曲线中存在鞍节点分岔、倍周期分岔和Hopf分岔。用相平面图和傅立叶谱对周期加倍现象进行了表征。此外，IHB方法的解析结果与数值积分结果吻合较好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Nonlinear Dynamics 工程技术-工程：机械

CiteScore

4.00

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.