Solution of viscously damped linear systems using a set of load‐dependent vectors

Harn C. Chen; Robert L. Taylor

doi:10.1002/eqe.4290190503

journal article Jul 01, 1990

Solution of viscously damped linear systems using a set of load‐dependent vectors

Harn C. Chen Robert L. Taylor

Earthquake Engineering & Structural Dynamics Vol. 19 No. 5 pp. 653-665 · Wiley

View at Publisher Save 10.1002/eqe.4290190503

Abstract

AbstractThis paper considers a solution method for viscously damped linear structural systems which are subjected to transient loading. The equations of motion of such systems are written in a first‐order form. A solution subspace is generated using the damped dynamic matrix and the static deflection from the first‐order form of the equations of motion. Two convenient bases, Lanczos vectors and Ritz vectors, are constructed from this subspace. An approximate solution is then obtained by superposition of the Lanczos vectors or the Ritz vectors. In contrast to the traditional mode superposition method using complex eigenvectors, the Lanczos vectors or the Ritz vectors are less expensive to generate than the complex eigenvectors, yet yield comparable accuracy. In addition, there is no need for a static correction since the static deflection is already contained in our solution subspace. Numerical examples are presented to show the potential of using the Ritz vectors to compute responses of damped dynamic systems.

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References

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Metrics

13

Citations

13

References

Details

Published: Jul 01, 1990
Vol/Issue: 19(5)
Pages: 653-665
License: View

Authors

Asst. Prof. of Civ. Engrg., Univ. of California, Berkeley, Calif.

Cite This Article

Harn C. Chen, Robert L. Taylor (1990). Solution of viscously damped linear systems using a set of load‐dependent vectors. Earthquake Engineering & Structural Dynamics, 19(5), 653-665. https://doi.org/10.1002/eqe.4290190503

Solution of viscously damped linear systems using a set of load‐dependent vectors

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