Fundamental frequency of a corner-supported rectangular sandwich plate with the central lumped mass

Abstract

An efficient method of calculation of the fundamental frequency of a corner-supported composite sandwich plate having a lumped mass at its centre is proposed in this work. The corresponding dynamic problem is solved using the Hamilton principle and the Rayleigh-Ritz method. The panel is modelled using the first order shear deformation theory. The panel deflection and angles of rotation are approximated based on certain combinations of trigonometry functions. Application of the Rayleigh-Ritz method allowed the original system of equations to be reduced to a homogeneous system of linear algebraic equations of the seventh order with respect to unknown coefficients of approximating functions. The fundamental frequency is found as a minimum eigenvalue of this system. Using this solution, the effects of the geometric parameters of the panel and the value of lumped mass were investigated. The results of the calculations were successfully verified by comparisons with the outcomes of the finite-element computations. The efficiency of the proposed methodology was demonstrated in the design analysis of the corner-supported composite sandwich panel with the central lumped mass subject to a constraint imposed on the value of fundamental frequency.