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

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 Hamiltonʹs 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 Galerkinʹs method is used to reduce the equations of motion to a set of non-dimensional coupled Mathieu–Hillʹs 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 Hsuʹs 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.