Free Vibration Analysis of Laminated Soft Core Sandwich Plates

Abstract

Free vibration behavior of laminated soft core sandwich plates with stiff laminated face sheets is investigated using a new C0 finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement variations are considered to be cubic for both the face sheets and the core, while the transverse displacement is assumed to vary quadratically within the core and remains constant in the faces beyond the core. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for an accurate modeling of laminated sandwich plates. As very few elements based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to develop this new element. The nodal field variables are chosen in such a manner to overcome the problem of continuity requirement of the derivatives of transverse displacements, i.e., no need to impose any penalty stiffness in the formulation. A nine node C0 quadratic plate finite element is implemented to model the HOZT for the present analysis. A new C0 element has been utilized to study some interesting problems on free vibration analysis of laminated sandwich plates. Many new results are also presented which should be useful for future research.