Analysis on Bending Vibrations of a Thin Plate by Dividing with Non-orthogonal Segments Utilizing Higher-order-differentiable Mode Shape Function

Abstract

This research deals with a new analytical procedure on bending vibrations of a thin plate. The plate is divided into finite number of non-orthogonal segments. The mode shape function is introduced with the product of higher power series or power series and trigonometric function. The unknown coefficients of the mode shape function are substituted by the deflection and its higher derivatives at each node of segments, which enables to satisfy both continuity and boundary conditions at the node of segment. The collocation method is used to satisfy the continuity of the derivatives of the deflection at the side of segments. Discretized equations of motion of the plate are derived with Galerkin method. Natural frequencies and modes of vibration are calculated with and without collocation method. By using the collocation method, continuity of space derivative of deflection between two adjacent segments are satisfied, which enables to obtain good agreement between the present results of natural frequencies and the exact ones.