功能梯度复合材料圆柱壳基本理论及长壳固有振动解

BASIC THEORY OF FUNCTIONALLY GRADED MATERIAL CYLINDRICAL SHELL AND NATURAL VIBRATION OF LONG SHELL

本文首先在功能梯度复合材料圆柱壳基本理论上将原始三维变系数控制方程转化为特殊类型各向异性及薄膜-弯曲耦联的二维常系数方程;对相当长圆柱壳提出轴向、周向分离变量振型函数,求取满足基本微分方程的固有振动解析解,得到功能梯度圆柱壳固有频率与振型分析的一般性方法,适用于任意功能梯度分布复合材料长圆柱壳。

Upon the basic theory of functionally graded material cylindrical shell, the original 3-D foundational equations with variable coefficients are transformed into anisotropic and membrane-bending coupling 2-D equations with constant coefficients. The separation-of-variables mode shape functions in axial and circumferential directions for long enough cylindrical shells are proposed for the analytic solutions, which satisfy the basic differential equations of natural vibration. The general approach is presented in the paper for the solutions of natural frequency and mode shape of functionally graded cylindrical shells which can be applied to long cylindrical shells with any kind of functionally graded material.