引用本文: 陈立群. 振动力学基础课程中的非线性振动. 力学与实践, 2023, 45(6): 1382-1384.
Chen Liqun. Nonlinear oscillations in fundamental course of vibration. Mechanics in Engineering, 2023, 45(6): 1382-1384.
 Citation: Chen Liqun. Nonlinear oscillations in fundamental course of vibration. Mechanics in Engineering, 2023, 45(6): 1382-1384.

## NONLINEAR OSCILLATIONS IN FUNDAMENTAL COURSE OF VIBRATION

• 摘要: 本文总结在振动力学基础课程教学中对非线性振动的处理。教学目的是了解最基本的非线性振动近似分析方法和典型非线性振动现象。主要内容包括谐波平衡法、非线性受迫振动中的跳跃现象、自激振动、内共振中的饱和和双跳跃、整星缩比模型的非线性能量汇减振和圆环的非线性隔振。结合实例说明建模和分析过程中的简化、力学的应用性和力学与数学的密切关系。

Abstract: The treatment of nonlinear oscillations is explored as a part of the fundamental course of vibration mechanics. The teaching goal is to understand a basic approximate analytical method in nonlinear oscillations and typical nonlinearly oscillating phenomena. The main contents include harmonic balance method, jump phenomenon in nonlinear forced oscillations, self-excited vibrations, saturation and double jumping in internal resonance, nonlinear energy sink for scaled whole-spacecraft vibration reduction and circular nonlinear vibration isolation via ring. The case studies are adopted to highlight simplifications in modeling and analysis, applicability of mechanics, and a close affinity between mathematics and mechanics.

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