摘要
分析了薄壁圆柱壳在纯弯曲下的非线性自由振动。基于改良的Brazier简单理论,将圆柱壳的纯弯曲变形简化为以下两个阶段:第一阶段壳体没有弯曲,横截面由圆形变成椭圆形;第二阶段壳体是横力弯矩作用下的变截面梁。通过Brazier简单理论获得壳体的应变能,然后利用拉格朗日方程求得薄壁圆柱壳的几何非线性自由振动方程,最终得到自由振动频率,并对线性解与非线性解进行对比分析。
The non-linear free vibration of thin-walled cylindrical shells under pure bending is analyzed. Based on themodified Brazier simple theory, deformation of the shell subjected to pure bending can be simplified to two stages. One isthat the sections of the shell become elliptic but its axis remains straight; the other is the transverse bending deformationwith the shell regarded as a beam with variable elliptic sections. The strain energy of the shell can be obtained based on theBrazier simple theory, and the non-linear free vibration equation of the thin-walled cylindrical shells will be derived by theLagrange equation. As a result, the free vibration frequency is obtained, and the linear and nonlinear solutions are comparedmutually
出处
《噪声与振动控制》
CSCD
2014年第6期29-32,共4页
Noise and Vibration Control
关键词
振动与波
自由振动
非线性
拉格朗日方程
vibration and wave
free vibration
nonlinearity
Lagrange equation
