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

✍ Scribed by Harn C. Chen; Robert L. Taylor

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 728 KB
• Volume: 19
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.4290190503

✦ Synopsis

This 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. '=[ 0 M] and (4) Equation ( ) is not the only first-order form of equation (I); however, it is appropriate to our purpose.