壁厚不连续不对称圆柱壳和开口壳的自由振动分析

视壁厚不连续不对称的圆柱壳或开口壳为层合壳。以弹性力学中的Hamilton正则方程为基础,分别应用Hamilton正则方程的半解析法构建层合壳每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性,联立各层的方程得到系统的控制方程和特征方程。主要的优点是系统的控制方程不限制圆柱壳的厚度,数学模型和数值方法也适应分析壁厚不连续且壁厚不对称的复合材料层合壳问题。

FREE VIBRATION ANALYSIS OF CYLINDRICAL SHELLS AND OPEN SHELLS WITH THICKNESS DISCONTINUITY AND DISSYMMETRY

The cylindrical shells and open shells with discontinuity and dissymmetry in thickness are considered as laminated shells. Based on the Hamilton canonical equation for elastic bodies, and using its semi-analytical solution, the linear equation for each layer of laminated shells is established respectively. The compatibility of displacements and stresses on the interface between layers is applied to derive the equation of the whole structure as well as the characteristic equation of natural frequencies. The major advantage of the proposed method is that it imposes no limit on the thickness of shells. The model and numerical method in this paper are also suitable for the problems of the composite laminated shells with discontinuity and dissymmetry in thickness.