Three-dimensional vibration analysis of sandwich and multilayered plates with general ply stacking sequences by a spectral-sampling surface method

This paper investigates the three-dimensional (3-D) vibration characteristics of sandwich and multilayered plates with general ply stacking sequences and arbitrary restraints based on a spectral-sampling surface method. The theoretical formulation is undertaken by the 3-D theory of elasticity such that it is able to study the dynamic behavior of sandwich and multilayered plates very well, even in the presence of soft layers. Under the current framework, a set of sampling surfaces along the thickness direction of each plate layer are primarily selected and the displacements of these surfaces are chosen as basic plate variables. Consequently, vibration solutions for sandwich and multilayered plates with different thicknesses, material properties and ply stacking sequences can be derived up to desired accuracy by selecting sufficient number of sampling surfaces. In addition, the penalty technique and Lagrange multiplier method are adopted to relax the enforcement of the boundary conditions. As a result, the proposed formulation can be applied efficiently to the 3-D vibration analysis of sandwich and multilayered plates with general restraints. The final solutions are determined by a modified variational principle, in which each of the basic plate variables is approximated by the spectral method. Results show that the present method is capable of calculating highly accurate numerical results for thick sandwich and multilayered plates with general ply stacking sequences and arbitrary boundary conditions.