Nonlinear Vibration of Parametrically Excited Viscoelastic Moving Belts, Part II: Stability Analysis

Abstract

The amplitude and existence conditions of nontrivial limit cycles are derived in the companion paper by the use of the method of multiple scales. In this paper, the stability for parametrically excited viscoelastic moving belts is studied. Stability boundaries of the trivial limit cycle for general summation parametric resonance are obtained. The Routh-Hurwitz criterion is used to investigate the stability of nontrivial limit cycles. Closed-form expressions are found for the stability of nontrivial limit cycles of general summation parametric resonance. It is shown that the first limit cycle is always stable while the second limit cycle is always unstable for the viscoelastic moving belts. The effects of viscoelastic parameters, excitation frequencies, excitation amplitudes, and axial moving speeds on stability boundaries are discussed.