Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Associate Professor Junhong Yue,Taiyuan University of Technology
Inviter:	Associate Professor Xu Wang
Title:	A linear finite element method for flexural waves on thin plates
Language:	Chinese
Time & Venue:	2023.07.06 15:00-17:00 N702
Abstract:	The study of vibration and fluctuation of thin plates has wide and important applications in the fields of aerospace and mechanical engineering. Mathematically, the vibration and flexural wave scattering problems of thin plates satisfy the fourth-order biharmonic wave equations, and their boundary conditions are more complicated, such as the clamped boundary conditions, which make their numerical calculation more difficult. Therefore, this talk mainly considers the numerical simulation of the eigenvalue problem of bounded thin plates and the cavity scattering problem of flexural waves in infinite thin plates. First, the fourth-order biharmonic wave equations are transformed into two lower-order equations by two ways: (1) operator decomposition method; (2) Ciarlet-Raviart mixed formulation. Meanwhile, the corresponding transparent boundary conditions are constructed for the flexural wave scattering problem. Then, the linear finite element methods with penalty terms are proposed to solve these two types of problems. Numerical examples show that the proposed method can effectively suppress the oscillations of the auxiliary variables on the clamping boundary and improve the stability and accuracy of the solution. These numerical studies will help to understand the vibration mode and flexural wave propagation behavior of thin plates to assist in the design and fabrication of novel structures.