Equipment Representations for Shock Calculations: Time Domain Dirichlet to Neumann Maps

Abstract

Abstract Large scale dynamic simulations can often be simplified by appropriately replacing large portions of the domain by a Dirichlet to Neumann, or DtN map (Givoli, 1992). Here we consider the problem of representing a dynamical subsystem, a piece of equipment aboard a naval vessel for example, in terms of an equivalent time domain DtN map. The exact DtN map is computed as a modal summation. The exact map is then approximated in both the low and high modal density regimes. The approximate DtN in the high modal density limit is computed utilizing fuzzy-structures concepts recently developed by Pierce, Sparrow and Russel (1993) and others. The resulting DtN map depends on just two easily determined system parameters: the total mass and the high-frequency stiffness.