Hamilton canonical equation for elastic bodies and natural frequencies analysis of integral stiffened plates

Abstract: Based on Hamilton canonical equation theory for elastic bodies, a novel mathematic model for the natural frequencies analysis of integral stiffened plates is achieved. Basic idea is the separate consideration of plate and stiffeners, i.e. 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 then the characteristic equation on natural frequencies. The advantages are the transverse shear deformation and rotary inertia are considered naturally, further more, without any limit to the thickness of plate and height of stiffener. The convergence studies of several numerical examples and results show that present method is reliable. The method in this paper can be easily developed to solve the corresponding problems of stiffened shells stiffened piezolaminated plates, and plates or shells with piezoelectric material patches.