强非线性振动系统的通用化求解程序及应用

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (8) : 1-4.

论文

强非线性振动系统的通用化求解程序及应用

张琪昌1,2, 赵蔷薇1, 王炜1,2

作者信息 +

Universal solving program and Application in the strongly nonlinear oscillation system

Zhang Qi-chang1,2, Zhao Qiang-wei1, Wang Wei1,2

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文章历史 +

摘要

基于研究强非线性振动系统的待定固有频率法，应用Mathematica符号运算语言，编写了适用于计算多自由度系统稳态渐近解的通用化程序。在将传统理论向高维复杂系统进行推广的同时，进一步实现了应用过程中涉及常微分耦合系统简化、高阶规范形计算等具体运算环节的系统化与程序化，极大地提高了理论推导的效率。基于文中提出的程序化方法，研究一类碳纳米管强非线性振动系统，计算了其规范形和稳态渐近解，并据此讨论了阻尼系数和激振力对于振动幅值的影响。最后将定量分析结果与数值结果进行对比，验证了程序化方法的有效性。

Abstract

The universal solving procedure to calculate steady-state asymptotic solution of strongly nonlinear vibration system with multi-degree of freedom was presented, by using the undetermined fundamental frequency method and computer algebra Mathematica. With the aim of promoting traditional theory to high-dimensional complex systems, the systematization and routinization of coupled ordinary differential systems in application and calculation of higher order normal form was realized, which improved the theoretical derivation efficiently. A class of strongly nonlinear vibration of carbon nanotube system was researched for its normal form and steady-state asymptotic solution, and then the exciting force and damping effect for the vibration amplitude were discussed. Finally, the results of quantitative analysis and numerical results were compared to verify the effectiveness of the programming methodology.

导出引用

张琪昌; 赵蔷薇; 王炜;. 强非线性振动系统的通用化求解程序及应用 [J]. 振动与冲击, 2012, 31(8): 1-4

Zhang Qi-chang; Zhao Qiang-wei; Wang Wei;. Universal solving program and Application in the strongly nonlinear oscillation system [J]. Journal of Vibration and Shock, 2012, 31(8): 1-4