Free and Forced Vibration Analysis of Carbon/Glass Hybrid Composite Laminated Plates Under Arbitrary Boundary Conditions

Abstract

This paper presents the theoretical investigations on the free and forced vibration behaviours of carbon/glass hybrid composite laminated plates with arbitrary boundary conditions. The unknown allowable displacement functions of the physical middle surface are expressed in terms of standard cosine Fourier series and sinusoidal auxiliary functions to ensure the continuity of the displacement functions and their derivatives at the structural boundaries. Arbitrary boundary conditions are achieved through the introduction of an artificial spring technique. The first shear deformation theory and Lagrange equations are utilized to derive the energy expression, and the eigenvalue equations associated with free and forced vibration are obtained by Rayleigh-Ritz variational operations. Subsequently, these equations are then solved to determine the natural frequency, mode of vibration, and the steady-state displacement response under forced excitation. The new results are compared with those from references and finite element methods to verify the convergence, accuracy and efficiency of the analytical method. The effects of hybrid ratios, stacking sequences, lamination schemes, fibre orientation, boundary conditions and excitation force on the free and forced vibration behaviours of the carbon/glass hybrid composite laminated plates are analyzed in detail.