Parametric instability regions of three-layered soft-cored sandwich beam using higher-order theory

摘要

The purpose of the present work is to study the parametric instability of a three-layered, soft-cored, symmetric sandwich beam subjected to a periodic axial load. Due to soft core, the displacements of the top and bottom skins are different and hence, instead of using the classical theory a higher-order theory is used. Using extended Hamilton's principle and taking beam theory for the skins and a two-dimensional theory for the core, the governing equations of motion and boundary conditions are derived. A generalized Galerkin's method is used to reduce the equations of motion to a set of nondimensional coupled Mathieu-Hill's equations with complex coefficients. The parametric instability regions for simple and combination resonances are investigated for simply supported, clamped-guided, clamped-free riveted and clamped-free end conditions by modified Hsu's method. The influences of shear parameter; the core loss-factor and the ratio of core thickness to skin thickness on the zones of instability have been studied. This general analysis can be applied to sandwich beams with a flexible core and any type of construction. The results are compared with those reported for classical theories. (C) 2007 Elsevier Ltd. All rights reserved.