Vibration and damping analysis of sandwich viscoelastic-core beam using Reddy's higher-order theory

This paper presents a unified formulation for vibration and damping analysis of a sandwich beams made up of laminated composite face sheets and a viscoelastic core with arbitrary lay-ups and general boundary conditions. A modified Fourier-Ritz method is employed to derive this unified formulation based on Reddy's higher order shear deformation theory. In composite facings, the material couplings including bending-stretching, bending-twist, and stretching-twist as well as the Poisson's effect are taken into consideration. Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities, ensure and accelerate the convergence of the series expansions. This method can be universally applicable to laminated sandwich beams with classical boundaries, elastic boundaries and their combinations without any special change in the solution procedure. Both convergence and accuracy are discussed and this modified Fourier-Ritz method yields many new and accurate results at a low computational cost for various boundary conditions including general elastic boundaries. Furthermore, the effects of some key parameters such as ply configuration, layer number, moduli and thickness ratios on the natural frequency and loss factor are illustrated. Especially the effects of restraints from different directions on two ends of the sandwich beam are deeply investigated.