反对称铺设层合板动力问题的Hamilton体系及辛几何解法

基于ＹＮＳ层合格理论，建立反对称铺设层合板动力问题的Ｈａｍｉｌｔｏｎ正则方程，并采用共轭辛正交归一关系给出一对边简支，另一对边为任意支承层合板自振频率的精确解，数值算例讨论了长宽比，铺设角，层数及剪切修正系数的影响。

AN EXACT SYMPLECTIC SOLUTION FOR THE DYNAMIC ANALYSIS OF SHEAR DEFORMABLE ANTISYMMETRIC ANGLE-PLY LAMINATED PLATES

Based on the theory of the YNS laminated plate, and by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis ofshear deformable antisymmetric angle-ply laminated plates is derived. The problem is led to the mathematical frame of symplectic geometry and algorithms. The exact solution for the laminated plate with arbitury boundary conditions is also derived by using the ad joint ortho-normalized symplectic expansion method. Numerical resultS are presented emphasizing the effects of length/thickness ratio, arbitury boundary conditions, degrees of anisotropy, numbers of layers, ply-angles and transverse shear correction coefficients.