Strong SaS formulation for free and forced vibrations of laminated composite plates

The application of the sampling surfaces (SaS) method to the three-dimensional (3D) stress analysis of laminated composite plates is presented in a companion paper (Kulikov GM, Plotnikova SV. Strong sampling surfaces formulation for laminated composite plates. Compos Struct 2017;172:73–82). In this paper, we extend the strong SaS formulation to the 3D vibration analysis of laminated plates. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate unknowns. Such choice of unknowns with the use of the Lagrange polynomials in spatial approximations of displacements through the layer thicknesses leads to a robust laminated plate formulation. The feature of the proposed approach is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes it possible to minimize uniformly the error due to the Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D free and forced vibration analyses of laminated composite plates.