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弹性体的正则方程和加筋板的固有频率分析
引用本文:卿光辉,邱家俊,塔娜.弹性体的正则方程和加筋板的固有频率分析[J].力学学报,2004,36(6):749-756.
作者姓名:卿光辉  邱家俊  塔娜
作者单位:天津大学机械工程学院力学系, 300072
基金项目:国家自然科学基金资助项目(10072038)~~
摘    要:应用弹性力学的Hamilton正则方程理论和其半解析法,为整体加筋板的固有频率分析提出了一种新颖的数学模型. 采用同一种平面元素离散板和加强筋,并分别建立板和加强筋的线性方程组. 考虑到板和加强筋连接界面上应力和位移的连续性,联立板和加强筋的方程得到全结构的方程组和求解固有频率的特征方程. 主要优越性表现为:结构的旋转惯性、剪切变形等都得到了考虑,且不限制结构的板厚度和加强筋的高度. 多个数值实例的收敛分析和结果证明了方法是可靠的. 该方法很容易被修改用来分析加筋壳、加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳问题.

关 键 词:固有频率  整体加筋板  开孔加筋板  Hamilton正则方程  半解析法
修稿时间:2004年1月9日

Hamilton canonical equation for elastic bodies and natural frequencies analysis of integral stiffened plates
Na Ta.Hamilton canonical equation for elastic bodies and natural frequencies analysis of integral stiffened plates[J].chinese journal of theoretical and applied mechanics,2004,36(6):749-756.
Authors:Na Ta
Abstract:Based on Hamilton canonical equation theory and its semi-analytical solution for elastic bodies, a novel mathematical model for the natural frequencies analysis of integral stiffened plates is presented. The same plane element is used to discretize the plate and stiffeners, the linear equation sets of plate and stiffeners are established separately. The compatibility of displacements and stresses on the interface between the plate and the stiffeners is employed to derive the integral equation of structure, and the characteristic equation on natural frequencies. The main advantages are the transverse shear deformation and rotary inertia are considered naturally, and there is no restriction on the thickness of plate and height of stiffener. The convergence tests of several numerical examples and results show that present method is reliable. The method can be easily modified to analyze the problems of stiffened shells, stiffened piezolaminated plates, and plates or shells with piezoelectric sensor and actuator patches.
Keywords:natural frequency  integral stiffened plate  stiffened plate with holes  Hamilton canonical equation  semi-analytical solution
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