Unified-domain spectral Chebyshev method for dynamic analysis of composite plates with arbitrarily shaped inclusions

Abstract

This study introduces the meshless Unified-domain Spectral Chebyshev (USC) method to perform dynamic analysis for composite plates with inclusions of complex geometries. The proposed technique overcomes the limitations of the conventional modal analysis approaches relying on homogenization-based approximations or domain decomposition. The USC explicitly models the entire plate with the present discontinuities, eliminating approximation errors due to homogenization, while providing significant speed-ups compared to the standard component mode synthesis method when used with the spectral Chebyshev approach. The governing equations are derived using Hamilton’s principle and Reissner-Mindlin plate theory. Gauss-Lobatto sampling points are employed to capture both cross-sectional and arbitrary in-plane geometry of the inclusions. At each sampling point, weight values are assigned to represent the shape of the discontinuities. By imposing essential boundary conditions via projection matrices obtained through singular value decomposition, global stiffness and mass matrices are obtained for dynamic analysis. Comprehensive case studies were performed for different inclusion shapes/arrangements and boundary conditions to validate the accuracy of the proposed technique. The results demonstrate that the natural frequencies and mode shapes computed using USC are in close agreement with the ones taken from literature and obtained through finite element analyses.