Vibration of sandwich panels using {3,2}-order plate theory

This paper concerns the evaluation of fundamental natural frequencies and mode shapes of simply-supported sandwich panels using Navier-type solutions within the {3,2}-order equivalent single-layer theory. The kinematic assumptions of the theory are cubic in-plane displacements and a quadratic transverse displacement The theory also assumes a cubic distribution of the transverse normal stress that is continuous across the laminate. The Euler-Lagrange equations of motion and consistent boundary conditions are obtained from Hamilton's principle. The predictive capability of the theory is assessed for homogeneous, laminated composite, and sandwich panels. The fundamental natural frequencies are compared with previously published results for varying plate aspect ratio, length-to-thickness ratio, and material modulus.