STABILITY ANALYSIS OF PARAMETRICALLY EXCITED SYSTEMS USING SPECTRAL COLLOCATION

Abstract

The spectral collocation method is used to determine the stability of parametrically excited systems and compared with the traditional transition matrix approach. Results from a series of test problems demonstrate that spectral collocation converges rapidly. In addition, the spectral collocation method preserves the sparsity of the underlying system matrices, a property not shared by the transition matrix approach. As a result, spectral collocation can be used for very large systems and can utilize sparse eigensolvers to reduce computational memory and time. For the large-scale system studied (up to 40 degrees of freedom), the spectral collocation method was on average an order of magnitude faster than the transition matrix approach using Matlab. This computational advantage is implementation specific; in a C implementation of the algorithm, the transition matrix method is faster than the spectral collocation. Overall, the method proves to be simple, efficient, reliable, and generally competitive with the transition matrix method.