Free vibration analysis of rectangular thin plates with corner and inner cutouts using C1 Chebyshev spectral element method. (December 2022) - Wang, Jingxiong; Li, Hongjing; Sun, Guangjun; Han, Lu
Abstract: 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. Highlights: A novel higher-order C 1 continuous Chebyshev spectral plate element is proposed. Hermite functions based on nonuniformly distributed nodes are used to construct element. Comparison studies show that the proposed element has good convergence and accuracy. Free vibration of rectangular thin plates with various kinds of cutouts are analyzed. The effects of cutout size, location and eccentric ratio are investigated.