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

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.