Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models

A variable-kinematic Ritz formulation based on two-dimensional higher-order layerwise and equivalent single-layer theories is described in this paper to accurately predict free vibration of thick and thin, rectangular and skew multilayered plates with clamped, free and simply-supported boundary conditions. The main result is the derivation at a layer level of so-called Ritz fundamental nuclei for the stiffness and mass matrices which are invariant with respect to both the assumed kinematic model and the type of Ritz functions. In this work, products of Chebyshev polynomials and boundary-compliant functions are chosen as admissible trial set. After studying the convergence of the method, its accuracy is evaluated, in terms of frequency parameters and through-the-thickness distribution of modal displacements, by comparison with some reference results available in the literature. Results for sandwich plates with soft core are given for the first time, which may serve as benchmark values for future research.