一类双壳结构振动特性的半解析法

A SEMI-ANALYTICAL SOLUTION FOR THE VIBRATION CHARACTERISTICS OF A GROUP OF DOUBLE-SHELL STRUCTURES

以Hamilton正则方程的半解析法为基础,为一类双壳结构的振动特性提出了一种新的数学模型。基本步骤:(1)独立地建立内外壳和连接筋的线性方程组;(2)考虑到内外壳和连接筋的界面上的应力和位移的连续性,联立内外壳和连接筋的方程,从而得到全结构的方程组。主要优点是:采用了同一种Hamiltonian等参元离散壳和连接筋,结构的转动惯性、剪切变形等因素都得到了考虑,而且不限制壳的厚度和筋的高度;该方法象一般的有限元法一样适应复杂的边界条件和由多种材料构成的结构。本文的方法可推广用来研究加筋复合材料或加筋压电材料层合壳及相应的双壳结构的动力学问题。

Based on the semi-analytical solution of Hamilton canonical equation, a new mathematical model for the vibration characteristics of a group of double-shell structures is proposed. The basic steps are as follows： 1. the linear equations of inner shell, outer shell and stiffeners are established independently; 2. the compatibility conditions of displacements and stresses on the interfaces between the shells and the stiffeners are employed to derive the governing equations of the whole structure. The presented method possesses following advantages： i） the same Hamitonian isoparametric element can be used to discretize both shells and stiffeners; ii） the transverse shear deformation, the rotary inertia of the structure are all taken into consideration, furthermore, no limitations exist in the thickness of shell and the height of stiffener; iii） similar to finite element method, it can handle the cases of complex boundary conditions and multi-material compositions. The proposed method can also be easily generalized to solve the dynamics problems of stiffened composite laminated shells/double-shell structures, and stiffened piezolaminated shell/double-shell structures.