Spectral properties for the vibrational response of parametrically excited system

Abstract

The response spectra are helpful to understand the vibrational characteristics of linear system, and further could be used as important indications for the failure diagnosis and state detecting of the system. Due to the parametric excitation, the vibrational spectra of linear periodic system differ distinctly from that of the linear time-invariant system. Thus, utilizing the Sylvester’s theorem and Fourier series approximations, commonly used in the matrix decomposition, the spectral components for both the free and forced responses of linear parametrically excited system are obtained theoretically in the first part of the paper. The effects of system stability and damping on the response spectra are discussed in detail. Moreover, the external resonant condition for periodic system is found in the analysis. In the following part of the paper, spectral simulations for a spur gear pair under idle load (modeled as the free response) and fluctuating load (modeled as forced response) are done respectively to validate the theoretical results and illustrate the special frequency distributing features of periodic system intuitively.