基于时滞思想的一类非线性弹性杆结构动力行为的研究  

ASYPTOTIC BEHAVIOR FOR A NONLINEAR ELASTIC ROD BASED ON THE INERTIAL MANIFOLD WITH DELAY

作　　者：牛丽芳[1] 张建文[1] 段周波[1] 

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《动力学与控制学报》2016年第4期332-336,共5页Journal of Dynamics and Control

基　　金：山西省青年科技研究基金资助项目(2015021009)~~

摘　　要：基于时滞思想,利用改进的Galerkin方法,研究了一类非线性弹性杆方程的长时间行为.该方法将控制方程的解投影到由其线性算子的特征函数所张成的完备空间内,并截取有限阶模态来逼近真实解,从而将无穷维动力系统近似为有限维动力系统.根据时滞思想,构造了反映高、低阶模态关系的时滞表达式,使得在数值模拟过程中无需通过复杂数值积分即可直接获取高阶位移分量,从而降低了系统维数,缩减了计算量.对系统进行了数值模拟及分析,得到用较低的模态可描述系统解的最终状态.In this paper,based upon a new concept of the inertial manifolds with delay,a kind of nonlinear elastic rod is studied by an improved version of the nonlinear Galerkin method. This method was employed to project the solutions of the governing equations onto the complete space spanned by the eigen-functions of equation operators. With the truncation of modes to approach the solution,the original infinite dimensional dynamic system is approximated as a finite one. Furthermore,a time-delay expression which implies the interaction between higher and lower modes was constructed. With the time-delay expression presented,the higher displacement modes were obtained directly without a complicated numerical integration,resulting in a system with less degree-of-freedoms and reducing the computation time.

关 键 词：时滞惯性流形 非线性GALERKIN方法 非线性弹性杆 

分 类 号：O241.8[理学—计算数学]