Uncertainty quantification of nonlinear vibration response of the oscillator with double-sided unilateral spring

Abstract

The oscillator with a double-sided unilateral spring is a common nonlinear system that widely exists in the industry. In order to deepen the understanding of its vibration characteristics, uncertainty quantification is carried out. The uncertain responses of systems with multi-solution phenomena are difficult to be investigated by the non-intrusive interval method. Thus, a surrogate model based on normalized frequency is proposed. First, the solution of the vibration response is calculated by the harmonic balance method and the arc-length method. Then, the normalized frequency is proposed to transform the multi-solution problem into a single solution problem, which makes the uncertainty quantification easy to be carried out. Finally, the effects of different types of uncertain cases on the nonlinear responses of the oscillator with a double-sided unilateral spring are obtained.