Some error bounds and numerical experiments in modal methods for dynamics of systems

We present some error expressions for approximate modal solutions of viscously damped linear structural vibration equations; these approximations are calculated by a variety of modal techniques. Motivated by our numerical experience, we show the equivalence of some different modal solutions in the presence of classical damping and, in passing, we obtain a previously unremarked manifestation of this type of damping. We make some brief comments about obtaining error estimates and, finally, we show some numerical results for a standard test problem which illustrate properties of the modal solutions.