非线弹性梁的几何非线性幅频响应分析  

An Analysis of the Geometric Nonlinear Amplitude and Frequency Response of Non-linear Elastic Beam

作　　者：刘燕[1] 彭建设[1] 

机构地区：[1]西华师范大学物理与电子信息学院,四川南充637002

出　　处：《绵阳师范学院学报》2009年第11期36-40,共5页Journal of Mianyang Teachers＇ College

基　　金：四川省科技厅应用基础项目(NO.2006J13-166)

摘　　要：针对非线弹性梁的几何非线性振动方程,采用林滋泰德-庞加莱法将非线弹性控制方程摄动展开成几个线性控制方程,略去线性控制方程中的小参数项并对其无量纲化。针对不同边界条件梁取试函数,同时运用Galerkin原理,分离出时域函数简化方程,对简化方程进行首次积分得到其混合非线性自由振动频率解析解,并对材料参数B对频率响应的影响进行了讨论。从计算结果上看,不考虑B对频率响应的影响时,文中解析解与理论解吻合较好;考虑B对频率响应的影响后,随着材料参数B的增大,非线性振动的响应频率呈现出下降的趋势,B对非线性振动频率和位移响应的影响变得明显,此时B对非线性振动的响应频率的影响将不可忽略。For the geometrical non - linear vibration equation of the nonlinear elastic beam, non - linear elastic equations are expand into several linear perturbation equations with Linzitaide -Poincar6 method, in which the small parameters in the linear equations are omitted and nondimensionalized. Taking the trial function for beams with different boundary conditions and using Galerkin principle to isolate the simplified equation of time - domain function. And then first time integral for the simplified equation is done to obtain its hybrid analytical solution of the nonlinear free vibration frequency. The impact of material parameter B on the frequency response is also discussed. The result shows that without considering the impact of B on the frequency response, the analytic solution in the text agrees well with the theoretical solution; while considering the impact of B on the frequency response, with the increase of material parameter B, the nonlinear vibration response shows a downward trend in the frequency and the impact of B on the response of non - linear vibration frequency and displacement becomes apparent. At this time, the impact of B on the frequency response of nonlinear vibration should not be ignored.

关 键 词：梁 混合非线性 GALERKIN原理 幅频响应 

分 类 号：O302[理学—力学]