正交各向异性功能梯度材料开口圆柱壳的自由振动分析

区别于一般圆柱壳，开口圆柱壳沿周向是不封闭的，因此具有四个边界，本文根据轴向梁式振动和轴向曲拱振动特性对各种端部与侧边边界条件下的壳体提出统一的位移振型函数，并根据哈密顿原理建立了材料参数与空间坐标相关的正交各向异性开口圆柱壳的动力变分方程，求出了不同材料属性下开敞圆柱壳固有频率与振型解的一般解析表达式，适用于任意边界条件下不同材料的开敞圆柱壳自由振动分析．

Free Vibration Analysis of the Orthotropic Functionally Graded Open Cylindrical Shells

The dynamic variational equations of orthotropic functionally graded open cylindrical shells are established based on Hamilton principle, with its material parameters varying with spatial coordinates. A unified function for the displacement mode shape of the open shells with various boundary conditions at the two ends and the two lateral sides is proposed according to the axially beam and arch vibration characteristics, and the generalized analytical expressions of the natural frequency and the mode shapes are given. This result can be applied to the free vibration analyses of functionally graded open cylindrical shells with arbitrary material properties and different boundary conditions.