Long and finite time approximations of high modal density systems

Abstract

Our recent results concerning modeling of undamped structures with high modal density show that such structures can be replaced by very simple structures with damping. In the extreme case, a structure with infinitely many degrees of freedom can be replaced by a single mass-dashpot-spring system. When applied to a particular structure, however, such a model has a finite time of validity, predicted to be T=O(Δω)−1. Here, Δω represents the spacing of natural frequencies in the original structure. In this contribution, we present models valid for simulation times T≫(Δω)−1. The new models are based on long time rather than high modal density approximations. We show how the two models can be combined to form a single model which gives accurate results for all times.