Nonlinear resonance phenomena of panel-type structures

Forced vibrations are considered for the cases of shear-deformable plates with or without initial curvature. A dynamic nonlinear theory for layered panels is derived by means of the von Karman-Tsien theory, modified by the generalized Berger-approximation. Moderately thick panels with polygonal planforms are considered. The shell edges are assumed to be prevented from in-plane motions and are simply supported and a distributed lateral force loading is applied to the structure. Shear deformation is considered by means of Mindlin's kinematic hypothesis. In the special case of laminated panels composed of isotropic layers with physical properties symmetrically distributed about the middle surface, a correspondence to moderately thick homogeneous panels is found. Application of a multi-mode expansion in the Galerkin procedure to the governing differential equation, where the eigenfunctions of the corresponding linear plate problem are used as space variables, renders a coupled set of ordinary time differential equations for the generalized coordinates with (mixed) cubic and quadratic non-linearities. The nonlinear steady-state response of panels subjected to a time-harmonic lateral excitation is investigated and the phenomena of primary, superharmonic, and subharmonic resonances are studied by means. of the perturbation method of multiple scales. Numerical results are cast in the form of graphs with a structural parameter varying in a wide range. (C) 1998 Elsevier Science Ltd. All rights reserved.