Abstract:
The presence of complex subsystems can dramatically affect the dynamics of the main structure to which they are attached. Exactly modeling these subsystems, however, is often impossible. Here, replacing the substructure (say a piece of equipment) by an equivalent set of forces which react back on the main structure is proposed. 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. Local in time approximations to the convolution integral are obtained using Pade approximants. These yield a family of equipment representations. The simplest requires two measured equipment properties, though more information can lead to greater accuracy. Our approximate DtNs are validated numerically in finite-element simulations. [Work supported by ONR.]