Comparison of free vibration behaviors for simply supported and clamped T-shaped thin plate resting on Winkler elastic foundation

Abstract

The analysis of free vibration problems for thin plates is essential for the design of various structural systems. However, it is difficult to find analytical solutions due to the complexity of mathematical computing. Based on the symplectic superposition method, the T-shaped thin plate on the Winkler elastic foundation is divided into four sub-plates and are solved by using the symplectic eigen expansion method, and the modes and frequencies are studied. The method begins directly with the fundamental equations and undergoes a rigorous mathematical derivation without assuming the form of the solution beforehand. This approach helps circumvent the drawbacks associated with traditional semi-inverse solution methods. In addition, the theoretical calculation model and finite element analysis model of T-shaped thin plates on elastic foundation are established by using Mathematic software and ABAQUS software in present paper. It proves that the symplectic superposition method converges very fast and has a good consistency with the finite element simulation results. Results show that the boundary condition, foundation stiffness and aspect ratio have great influences on vibration frequency and mode shape for T-shaped structures.