Experiments and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions and uncertainties

Abstract

This paper presents experiments and numerical simulations of a nonlinear clamped-clamped beam subjected to external excitations and uncertainties. A coupling of the Harmonic Balance Method (HBM) with a non-intrusive Polynomial Chaos Expansion (PCE) is proposed in order to determine the dynamic response of the nonlinear structure. The system studied is a steel beam bonded on both sides to a heavy steel block. First of all, increasing and decreasing swept sine experiments are performed in order to show the presence of jumping points in the vicinity of the primary resonance. From the swept-sine experiments, we use a signal processing tool to extract the experimental multi-harmonic frequency response of the structure. Secondly, a numerical method, called the Harmonic Balance Method (HBM), is used to simulate the deterministic vibrational stationary response of the nonlinear clamped-clamped beam. The input of the HBM is either a mono-harmonic signal to update the nonlinearities of the clamped-clamped beam or a multi-harmonic experimental signal to show the effects of the non-ideal input signal on the response. Finally, the quantification of uncertainty effects on the variability of the nonlinear multi-harmonic response is investigated by using a non-intrusive polynomial chaos expansion (PCE) alongside the Harmonic Balance Method (HBM). A new methodology was developed to split the simulated solutions into various intervals (i.e. various branches of continuous nonlinear solutions) in order to allow the PCE analysis to be performed despite the presence of returning points in the nonlinear response. The efficiency and robustness of the proposed methodology is demonstrated by comparison with Monte Carlo simulations.