Hamilton canonical equation for elastic bodies and natural frequencies analysis of integral stiffened plates
弹性体的正则方程和加筋板的固有频率分析

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.