用高阶位移模式分析复合材料层合板的自由振动

建立一种新的高阶位移模式：分层假设复合材料层合板的位移场，利用各层间应力及位移的连续性条件，导出了作为整体的层合板控制微分方程。最后，采用这一高阶剪切理论来分析复合材料矩形层合板的自由振动。数值计算采用有限差分法，并编制了计算程序，计算得出了六种不同边界条件、不同铺层、不同宽厚比工况下的矩形层合板的自振频率。同经典理论解进行比较，可以看出本文方法简便易行，且精度较高，可以在微机上实用。

THE FREE VIBRATION OF COMPOSITE LAMINATED PLATES ANALYZED WITH A HIGH-ORDER DISPLACEMENT MODEL

For the analyses of free vibration of composite laminated rectangular plates, a kind of high-order displacement model is suggested in this paper, which is shaped by firstly assuming the displacement field of each ply of the laminated plate then using the continuous conditions of stresses and displacements between the plies to form the governing differential equation of the whole body of the laminated plate, which is manifested as a high-order shear deformation theory. In the paper, the finite 'difference method is used to analyse the free vibration of the composite laminated plate. A computer programme is developed for the computation and computations can be carried out on a micro-computer. The fundamental frequencies of laminated rectangular plates with different boundary conditions, different plyings and different ratios of the length of side to thickness are all obtained. Comparisons of results are made with those obtained with the classical theoretical solutions. From the comparison, it may be concluded that the method in the paper is not complicated, having satisfactory precision and can be carried out on micro-computers.