Free Vibration Analysis of Rectangular Thin Plates with Corner and Inner Cutouts Using C1 Chebyshev Spectral Element Method

This paper presents a novel higher-order C-1 continuous Chebyshev spectral element method for the free vibration analysis of rectangular thin plates with corner and inner cutouts. To achieve C-1 continuity at the interfaces of adjacent elements, the Hermite interpolation functions through nonuniformly distributed Chebyshev nodes are employed to construct the element displacement field. A Gauss-Lobatto type quadrature is used to efficiently evaluate the element matrices. Comparison with other well-established methods show that the proposed element has good convergence and accuracy. The influence of cutout size, location and eccentric ratio on the natural vibration characteristics of plates are investigated.