A complete symplectic approach for a class of partial differential equations arising from the elasticity
A complete symplectic approach for a class of partial differential equations arising from the elasticity
复制标题
由弹性引起的一类偏微分方程的完全辛方法
DOI：
10.1016/j.apm.2020.08.002
复制
发表时间：
2021
影响因子：
5
通讯作者：
Chen Alatancang
中科院分区：
文献类型：
--
作者：
Qiao Yanfen;Hou Guolin;Chen Alatancang
The symplectic approach is used to establish the unified framework for solving governing equations of some thin plate problems in elasticity. By introducing appropriate functions, the given partial differential equation is first transferred into a separable Hamiltonian system. The completeness of the system of generalized eigenvectors of corresponding Hamiltonian operator matrix is proved, which serves as the theoretical foundation of symplectic approach. Utilizing the expansion theorems, the general solutions of the boundary value problem for partial differential equation under consideration are obtained. Moreover, the bending, buckling, and free vibration problems of fully clamped rectangular thin plates governed by the given partial differential equation are solved analytically by the technique of superposition. Numerical results for bending, buckling, and free vibration plates are presented to demonstrate the availability and validity of the approach by comparison with those available in the literatures.
