The Earthquake Engineering Online Archive

Solution of Viscously Damped Linear Systems Using a Set of Load-Dependent Vectors

Chen, Harn-Ching; Taylor, Robert L.

UCB/SEMM-1988/16, Dept. of Civil Engineering, University of California, Berkeley, 1988-08, 24 pages (500/C23/88/16)

The paper considers a solution method for viscously damped linear structural systems subjected to transient loading. Equations of motion of such systems are written in a first-order form. A Krylov subspace is generated using damped dynamic matrix and the static deflection from the first order form of the equation of motion. Two convenient bases, Lanczos and Ritz vectors, are constructed from the Krylov subspace. An approximate solution is then obtained by superimposition of the Lanczos vectors on the Ritz vectors.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-88-16.pdf (8 MB)