Dynamic stiffness formulation for in-plane and bending vibrations of plates with two opposite edges simply supported

Abstract

A dynamic stiffness formulation is developed for both in-plane and bending vibrations of plates with two opposite edges simply supported. The bending motions of plates are described in terms of Leissa’s displacement functions while the in-plane motions take the forms take the forms that were proposed by Bercin and Langley. Using Projection Method, the forces and their corresponding displacements along plate junctions are projected onto a set of orthogonal functions, by which means the well-known spatial dependence difficulties can be overcome, and, as a result, local dynamic stiffness matrix is obtained. Classical finite element technique is utilized to assemble local stiffness matrix into global coordinates. Finally, dynamics of an L-shaped plate is addressed, within which conversion of in-plane and bending motions occurs. Our numerical results are in good agreement with those obtained from finite element method, which demonstrates that this dynamic stiffness formulation has great potential in modeling the dynamics of built-up plate structures, especially in characterizing the in-plane waves, bending waves, and their mutual conversions along plate junctions.