344 / 2019-09-30 22:46:11

四边固定薄板自由振动的辛方法研究

rectangular plate; static bending;free vibration; symplectic solution

结构优化与结构行为分析 > 结构力学行为分析

In this paper, free vibration of a rectangular plate with all edges clamped is analyzed in the Hamiltonian system. First, the symplectic governing equations
are established for static bending problems. Second, the eigenvalues and eigenvectors are obtained for the static bending of rectangular plate. The deflection for vibration are supposed based on the linear superposition of the static form of the deflection for thin plate with two opposite sides clamped.
Last, the Lagrange function is minimized by Rayleigh-Ritz method. Thus, the free vibration problem is transformed into general matrix characteristic problem. The natural frequencis are yielded for plates with different aspect ratios. The effectiveness of the proposed method is vadalidated by comparsion the obtained results with the analytical results.