High modal density approximations for equipment in the time domain

摘要

This article considers modeling the effect of complex subsystems on the dynamics of the main structure to which they are attached. it is proposed that the substructure (say a piece of equipment) be replaced by an equivalent set of forces which react back on the main structure. These forces are given as time convolutions of the displacements at the equipment attachment points. The convolution integral, which represents a time domain DtN (Dirichlet-to-Neumann) map, is approximated in the high modal density limit with determined error bounds. This approximation leads to a family of equipment representations. The simplest requires few measured equipment properties, though more information can lead to greater accuracy. Our approximate DtNs are demonstrated numerically in finite element simulations.