New approaches for non-classically damped system eigenanalysis

This paper presents three new approaches for solving eigenvalue problems of non-classically damped linear dynamics systems with fewer calculations than the conventional state vector approach. In the latter, the second-order differential equation of motion is converted into a first-order system by doubling the size of the matrices. The new approaches simplify the approach and reduce the number of calculations. The mathematical formulations for the proposed approaches are presented and the numerical results compared with the existing method by solving a sample problem with different damping properties. Of the three proposed approaches, the expansion approach was found to be the simplest and fastest to compute. Copyright © 2005 John Wiley & Sons, Ltd.