Differential Cubature Method for Free Vibration Analysis of Arbitrary Shaped Thick Plates
Wu Lanhe, Zhao Yongmao, Li Yanqiang
(Shijiazhuang Railway Institute, Shijiazhuang, 050043)

Abstract: In this paper, a new numerical solution technique, the differential cubature method is applied to solve the free vibration problems of a rbitrary shaped thick plates. The basic idea of the solution technique is to express a linear differential operation such as a continuous function or any orders of partial derivatives of multi-variable function as a weighted linear sum of discrete function values chosen within the overall domain of a problem. By using the differential cubature procedure, the governing differential equations and boundary conditions are transformed into sets of linear homogeneous algebraic equations. This is an eigenvalue problem, of which the eigenvalues can be calculate d numerically. The subspace iterative method is employed in search of the free vibration frequency parameters. Detailed formulations are presented, and the method is examined here for its suitability for solving the vibration problems of moderately thick plates governing by the Mindlin shear deformation theory. The applicability, efficiency and simplicity of the method are demonstrated through solving some example plate vibration problems of different shapes. The numerical ac curacy of the method is ascertained by comparing the vibration frequency solutions with existing literatures.
Keywords: differential cubature method, free vibration, natural frequency, thick plate with arbitrary shape.