Inverse iteration for damped natural vibration

Abstract

Inverse iteration is extended to internally and/or externally damped natural vibration. Each iteration involves one matrix multiplication and one linear equation solution of order <i>n</i>. The symmetric band form of the original undamped eigenvalue problem is preserved. If the undamped mode is taken as the first approximation, the inverse iteration will converse to the corresponding damped mode in about four iterations. However, the one step method is divergent for heavy damping. Therefore, it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations. The method is successful for both discrete systems and distributed systems. The implementation is very simple by means of complex arithmetic which is readily available in many FORTRAN compilers.