Effect of extreme in-plane and transverse stiffness ratios on frequencies and load transfer between face sheets and core of rectangular sandwich plates

Abstract

Challenging issues for sandwich structures include accurately finding their frequencies and how the load transfers from face sheets to the core when their material stiffness ratio (FCSR) in either the axial or the transverse directions varies from 1 to 107. Here we use both the equivalent single layer and the layer wise shear and normal deformable plate theories to analyze problems for rectangular plates of different thickness/length ratios. The Ritz method with Jacobi polynomials as basis functions is employed to numerically solve three-dimensional linear elasticity theory equations. Transverse stresses are calculated using a one-step stress recovery scheme. It is found that the FCSR in the transverse direction determines the minimum degree of complete polynomials in the thickness coordinate needed to accurately compute the lowest six frequencies and the transverse stresses. New results include the following: (i) the FCSR in the transverse direction has a greater influence than that in the axial direction on the computed frequencies and transverse stresses, and (ii) whereas both transverse normal and shear stresses in the core contribute to transmitting loads between the two face sheets for FCSR < 103, however, only the former is effective for FCSR ≥ 105.