Analysis of the convergence properties of Rubenstein's method for the determination of the lower modes of vibration of a multi-degree of freedom system

This paper analyzes the convergence properties of a method, recently proposed by Rubenstein, for the determination of the lower modes of vibration of a multi-degree of freedom system from a reduced eigenvalue problem. It is shown that under certain conditions the method converges to the exact eigenvalues. It does not have global convergence and hence some care must be exercised when using it.