Analysis on Nonlinear Forced Vibrations of a Thin Shell-panel Including Clamped Edges

Abstract

This research deals with analytical results on nonlinear forced vibrations of a thin shell-panel including clamped edges．At the boundaries of two opposite edges, the shell-panel is simply supported, and at the other two edges the panel is simply supports or clamped．Coordinate function of deflection is assumed with the product of power series and trigonometric function．Neglecting the effect of in-plane inertia force, the Donnell type equations are applied as the governing equations of the shell-panel．Stress function is introduced to satisfy compatibility equation and in-plane boundary condition ,Applying the Galerkin procedure, equation of motion is reduced to a set of nonlinear ordinary differential equations．Nonlinear periodic responses of thin shell-panel with various curvatures including clamped edges are analyzed using the above calculation method under periodic excitation force with the harmonic balance method．