Abstract
For linear structural systems it is possible to use the undamped eigenvectors or load-dependent Ritz vectors to produce a set of modal response equations. When arbitrary viscous damping exists the modal equations are coupled with the modal damping matrix. A robust and efficient numerical algorithm is presented, which solves the coupled modal equations by iteration. It is shown that the numerical integration algorithm always converges. The method produces an exact solution for proportional damping and for loading that varies linearly within an arbitrary time interval. In addition, the algorithm has been modified to incorporate automatically the mode acceleration method and periodic loading. Two numerical examples are presented to illustrate the practical application of the algorithm. A FORTRAN listing of a subroutine is given to facilitate easy implementation of the method in existing computer programs for dynamic response analysis.
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