强非线性振动系统的通用化求解程序及应用  

Universal solving program and its Application in a strongly nonlinear oscillation system

作　　者：张琪昌[1,2] 赵蔷薇[1] 王炜[1,2] 

机构地区：[1]天津大学机械学院,天津市非线性动力学与混浊控制重点实验室,天津300072 [2]天津大学内燃机燃烧学国家重点实验室,天津300072

出　　处：《振动与冲击》2012年第8期1-4,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(10872141;11072168);天津市自然科学基金(11JCYBJC05800)

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,计算其规范形和稳态渐近解,并据此讨论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。The universal solving procedure to calculate steady-state asymptotic Solution to a strongly nonlinear vibration sysiem with multi-degree of freedom was presented by using the undetermined natural frequency method and the computer algebra of Mathematiea. With the aim of promoting the 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, they improved the theoretical derivation efficiency. A class of strongly nonlinear vibration of a carbon nanotube system was studied for its normal form and steady-state asymptotic solution, and then the effects of exciting forces and damping coefficients on the vibration amplitude were discussed. Finally, the results of the quantitative analysis and the numerical results were compared to verify the effectiveness of the programming methodology.

关 键 词：高维系统 强非线性振动 规范形 稳态响应 

分 类 号：O322[理学—一般力学与力学基础]