粘弹性复合材料屈曲梁非线性参数振动的稳定性和分岔分析  

Stability and bifurcation of a parametrically excited viscoelastic composite buckled beam

作　　者：曾志刚[1] 叶敏[1] 

机构地区：[1]浙江大学航空航天学院力学系,杭州310027

出　　处：《振动与冲击》2012年第2期129-135,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(10672141)资助项目

摘　　要：在之前的研究中我们以ABS树脂为基材,填充1%～10%的金红石纳米二氧化钛制成纳米复合材料系列梁样本,并搭建了参数激励非线性振动实验系统。采用实验建模的方法,建立了粘弹性屈曲梁的动力学控制方程。在此基础上,进一步研究了系统的稳定性和分岔特性,利用多尺度方法对系统的幅频响应和解的稳定性进行了分析,并采用数值模拟分析参数激励幅值对系统分叉行为的影响,同时研究了系统通往混沌的道路,获得了丰富的动力学现象。A series of composite materical samples were synthesized by using acrylonitrile-butadine styrene copolymer（ABS） resin as basic material and adding rutile nanscaled titania from 1% to 10% as reinforced material.A test platform for nonlinear parametrically excited vibrations was set up.Adopting a modeling method with tests,the dynamic governing equation of a viscoelastic composite beam was built.Furthermore,the stability and bifuraction of the system were further discussd.The multi-scale analysis method was used to analyze the amplitude and frequency response characteristics of the system and the stability of the solutions to the dynamic equation.The effect of the parametric excitation amplitude on the bifurcation behavior of the system was analyzed with numerical simulation.The way to chaos for the system was studied.The results showed that there are rich nonlinear dynamic pehnomena in the system.

关 键 词：粘弹性屈曲梁 参数激励 非线性振动 稳定性 分岔 混沌 

分 类 号：O322[理学—一般力学与力学基础]