A synthesis formulation of explicit damping matrix for non-classically damped systems

In computing the dynamic response of a connected system with multiple components having dissimilar damping characteristics, often referred to as non-classically damped system such as nuclear power plant piping systems supported by stiff structures, one needs to define the system-level damping based upon the damping information of components. This paper presents a general formulation for computing rigorous explicit damping matrices for multiply connected, non-classically damped, coupled systems. The algorithm derived was based on a synthesis process developed by Hurty [AIAA J. 3 (4) (1965)], in which three different kinds of damping were utilized to describe the energy dissipation of the system. It was also shown that the system damping developed by the synthesis approach could reduce to damping formulations available in the literature such as those of Gupta et a. [Seismic response of non-classically damped systems. Nucl. Eng. Design, vol. 91, 1986] and Pajuhesh et al. [Determination of composite damping matrices. In: Proceedings on Fifth World Conference on Earthquake Engineering, vol. 1, 1973] when the same assumptions were applied for the interface connectivity. The method presented in this paper was used in developing the rigorous system matrices for the BNL solution to a set of benchmark problems analyzed in the NRC-BNL benchmark program for the evaluation of the state-of-the-art methods and computer programs for non-classically damped systems [Benchmark Program for the Evaluation of Methods to Analyze Non-Classically Damped Coupled Systems (2000)]. The details of the NRC-BNL benchmark program are presented in a companion paper [A NRC-BNL Benchmark Evaluation of Seismic Analysis Methods for Non-Classically Damped Coupled Systems (in press)]. (C) 2003 Elsevier B.V. All rights reserved.