The Earthquake Engineering Online Archive

Properties and Solutions of the Eigensystem of Nonproportionally Damped Linear Dynamic Systems

Chen, Harn-Ching; Taylor, Robert L.

UCB/SEMM-1986/10, Dept. of Civil Engineering, University of California, Berkeley, 1986-11, 32 pages

This report reviews currently available methods for solving dynamic response of nonproportionally damped linear structural systems. A general condition in which the system is not limited to be lightly damped is considered to accommodate the possibility of various applications. Mode superposition is used to evaluate the response of the system subjected to initial conditions and external loadings. For this purpose, the subspace iteration technique is extended to extract the least dominant set of eigensystems. The iteration vectors are modified in such a way that only real arithmetic is employed when dealing with complex vectors. Hence, both storage space and computation time are reduced tremendously for the extraction of the damped modes.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-86-10.pdf (1 MB)