A semi-analytical model for dynamic analysis of non-uniform plates

Dynamic properties of the plate structures can be enhanced by introducing discontinuities of different kinds such as using surface-bonded discrete patches or spatially varying the stiffness and mass properties of the plate. Fast and reliable design of such complex structures requires efficient and accurate modeling tools. In this study, a novel semi-analytical model is developed for the dynamic analysis of plates having discrete and/or continuous non-uniformities. Two-dimensional Heaviside unit step functions are utilized to represent the discontinuities. Different from existing numerical methods based on Heaviside functions, a numerical technique is proposed for modeling the discontinuities that are not necessarily aligned with the plate axes. The governing equations are derived using Hamilton's principle and Rayleigh–Ritz method is used for determining the modal variables. The surface-bonded patches are used to demonstrate discrete non-uniformities where variable-stiffness laminates are selected to represent continuous non-uniform structures. Natural frequencies and mode shapes obtained using the proposed method are validated with finite element analyses and the existing results from the literature. The results show that the developed model performs accurately and efficiently.