各向异性矩形板自由振动的一般解析解法

根据各向异性矩形薄板自由振动横向位移函数的微分方程建立了一般性的解析解．该一般解包括三角函数和双曲线函数组成的解，它能满足4个边为任意边界条件的问题．还有代数多项式和双正弦级数解，它能满足4个角的边界条件问题．因此，这一解析解可用于精确地求解具有任意边界条件的各向异性矩形卞的振动问题．解中的积分常数可由4边和4角的边界条件来确定．由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶固有频率及其振型，以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论．

Free Vibration of Anisotropic Rectangular Plates by General Analytical Method

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution was established. This general solution composed of the composite solutions made by trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four comers. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four comers. Each natural kequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped was calculated and discussed.