Vibration of skew plates by the MLS-Ritz method

This paper presents a study on the vibration of skew plates by a numerical method, the moving least square Ritz (MLS-Ritz) method which was proposed by the authors in a previous study [Zhou L, Zheng WX. A novel numerical method for the vibration analysis of plates. Computational mechanics WCCM VI in conjunction with APCOM’04, Beijing, China, 5–10 September 2004; Zhou L, Zheng WX. MLS-Ritz method for vibration analysis of plates. Journal of Sound and Vibration 2006;290(3–5):968–90]. One of the most challenging numerical difficulties in analysing the vibration of a skew plate with a large skew angle is the slow convergence due to the stress singularities at the obtuse corners of the plate. The MLS-Ritz method is employed in this paper to address such problem. This method utilises the moving least square technique to establish the trial function for the transverse displacement of a skew plate and the Ritz method is applied to derive the governing eigenvalue equation for the skew plate. The boundary conditions of the plate are enforced through a point substitution technique that forces the MLS-Ritz trial function satisfying the essential boundary conditions along the plate edges. Due to the flexibility of the arrangement of the MLS-Ritz grid points, more grid points can be placed around the obtuse corners of a skew plate so as to address the stress singularity problem at the corners. A series of cases for rhombic plates of various edge support conditions are presented to demonstrate the efficiency and accuracy of the MLS-Ritz method.