有限元线法求解非线性模型问题——Ⅲ.薄膜的固有振动

ANALYSIS OF NONLINEAR MODEL PROBLEMS BY THE FINITE ELEMENT METHOD OF LINES—Ⅲ. FREE VIBRATION OF MEMBRANES

摘要: 本文是有限元线法(FEMOL)求解非线性模型问题的系列工作之三,对薄膜的固有振动这一特征值模型问题作了分析求解。文中,首先用FEMOL对特征值问题的泛函进行半离散,得到相应的常微分方程(ODE)特性值问题;然后,利用若干ODE变换技巧将问题转换成标准的非线性ODE问题;最后,采用一个新近研究出的有效算法,对各阶特征对进行了方便有效、精确可靠的求解。文中出示的算例展示了该法的功效。
- 有限元线法 /
- 非线性问题 /
- 特征值 /
- 固有振动
Abstract: As the third paper in this series of nonlinear applications of the finite element method of lines (FEMOL), the present paper applies this method to eigenvalue problems by presenting a FEMOL analysis of the free vibration of various membranes. Firstly, the vibration problem is discretized into eigenvalue problem in ODEs. Then using a number of ODE conversion techniques, the eigenvalue problem is further transformedinto a standard nonlinear ODE problem, which is solved by a recently -developed ODE eigen-solver. Numerical examples are given to show the present approach.
- FEMOL /
- nonlinear problem /
- eigenvalue /
- free vibration