Moderately large flexural vibrations of composite plates with thick layers

Abstract In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated.

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