Nonlinear vibration and dynamic instability analyses of laminated doubly curved panels in thermal environments

Abstract

Nonlinear dynamic analysis for a shear deformable anisotropic laminated doubly curved panel of rectangular planform resting on elastic foundations is presented. A new panel model of arbitrary curvature and arbitrary fiber stacking sequences but constant thickness is developed and established. The governing equations are based on an extended higher order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the anisotropic couplings. The nonlinear deformations and initial deflections of the panel are both taken into account. A two-step perturbation technique combining with the Galerkin method is employed to determine the linear and nonlinear vibration frequencies and forced responses. Nonlinear forced harmonic vibration in a Duffing oscillator for anisotropic laminated doubly curved panel is also investigated and discussed together with the effects of damping and excitation by using multiscale and Melnikov methods. The numerical results are validated for various lamination schemes through a comparison with solutions for free vibration frequencies of saddle (hyperbolic), flat plate, cylindrical and spherical shells available in the literature or obtained by the commercial finite element software. The numerical illustrations concern nonlinear vibration and dynamic response of moderately thick, anisotropic laminated doubly curved panels under different values of panel geometric parameters and mechanical excitation.