中文摘要：

考虑大挠度几何非线性和剪切变形的影响,工程中机械柔性板壳结构的非线性动力学运动控制方程经常被转化为二阶模态的、包含有二次和三次非线性项和外激励的非线性常微分方程,由于二次非线性项的存在,常用的多尺度法进行摄动分析时,需要复杂的运算才能将其包含进来。相比之下,基于傅里叶扩展和时间尺度的渐进摄动法可以较容易地将非线性动力学微分方程中的平方项考虑进来。通过引进适当的尺度变换,利用渐进摄动法对该系统在二阶模态之间发生1：2内共振、主参数共振、1/2亚谐共振时进行摄动分析,得到自治系统下的平均方程。数值结果发现4自由度自治系统存在复杂的周期运动、倍周期运动、概周期运动。该非线性系统为量纲一后的结果,对于与该系统类似的多自由度非线性机械系统可以直接用此平均方程进行全局分叉和混沌动力学研究。

英文摘要：

By considering the nonlinear strains-displacement relation and the effect of the shear deformation,the nonlinear governing equations of motion for the structure of plate and shell in the mechanical engineering are a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under external excitations.To consider the influence of the quadratic terms on the nonlinear dynamic characteristics of the nonlinear system,it is difficult for one to use the method of multiple scales to obtain the second-order approximate solution which includes the quadratic terms.By using the asymptotic perturbation method,based on the Fourier series and time rescaling,the quadratic terms can be included in the average equations.By introducing proper scale transformations,the asymptotic perturbation method is used to reduce the second-order non-autonomous nonlinear differential equations to autonomous nonlinear differential equations.The resonant case considered is 1：2,principal parametric resonance-1/2 subharmonic resonance.Then numerical analysis of the governing averaged equation is carried through by using Runge-Kutta method.It is found from numerical results that complex periodic,double-period and quasi-period motions exit intle four-degree-of-freedom system.