Boundary beam characteristics orthonormal polynomials in energy approach for vibration of symmetric laminates — II: Elastically restrained boundaries

Abstract

This paper presents an eigenvalue formulation for the vibration analysis of symmetrically laminated rectangular plates subjected to translational and rotational restraints at the edges. The Rayleigh-Ritz method, along with the deflection functions assumed in sets of orthogonally generated polynomials, is used to perform the analysis. The total strain energy of the elastically restrained rectangular plate is the sum of the bending strain energy and elastic strain energy of translational and rotational restraints. This resulting strain energy combined with the kinetic energy of the plate formed the total energy functional which is minimized to obtain the governing eigenvalue equation of the elastically restrained symmetrically laminated rectangular plate. In this paper, several examples of elastically restrained laminated plates with different fiber orientation angles and stacking sequences have been solved to demonstrate the accuracy and efficiency of the present method. The combined effects of laminate stacking sequences, fiber orientation angle and translational and rotational stiffnesses of the elastic edges on the vibrational response have been carefully examined.