周边固支深薄球壳的非线性动态分析

考虑几何非线性变形,推导深薄球壳非线性问题的位移型动力控制方程.将位移分解为动态项和静态项两部分,根据Hamilton原理,将无量纲偏微分方程组化为常微分方程组.利用打靶法进行数值求解,通过求得的数值结果讨论壳体的前三阶振动频率与壳体各参数之间的关系.结果表明壳体展开角较小时,高阶振动的频率大于一阶振动的频率.横向载荷对高阶振动频率的影响小于其对一阶振动频率的影响.

Nonlinear dynamic analysis of deep thin spherical shell with clamped edges

Taking the geometry nonlinear deformation into account,a displacement-type dynamic control equation was derived for the nonlinear problem of deep thin spherical shell.The displacement would be decomposed into two terms,one being the static and other being dynamic.According to Hamilton principle,the dimensionless partial differential equation would be transfered into ordinary differential equation.Shooting method was used for its numerical solution;and which was used further to discuss the relationship between shell’s first third-order vibration frequency and shell parameters.The result showed that the frequency of higher-order vibration was higher than the first order vibration frequency if the spread angle of the shell was smaller.Transverse load would have less influence on the higher-order vibration frequency than on the first order one.