Nonlinear vibrations of a beam with non-ideal boundary conditions and stochastic excitations - experiments, modeling and simulations

Abstract This paper presents experiments and numerical simulations of a nonlinear clamped-clamped beam subjected to stochastic broadband excitations. Broadband excitations are performed experimentally in order to show the hardening effect and the enlargement of the response peak in the vicinity of the primary resonance, and to detect the presence of secondary peaks resulting from the harmonics generated by the primary resonance. Using the decomposition of a random signal into a multi-harmonic periodic equivalent signal, the shooting method and the Harmonic Balance Method (HBM) are used to simulate the response of the nonlinear clamped-clamped beam subjected to a stochastic excitation. The latter is modeled as a multi-harmonic periodic equivalent signal in order to be used by both the shooting method and the HBM. A periodogram strategy is used to ensure a good estimate of the resulting Power Spectral Density (PSD). The two nonlinear methods are compared in terms of computation time and precision. A specific attention is paid on correct use of these methods. Finally, comparison between experiments and numerical simulations are performed for different levels of stochastic excitations. Good correlations are observed thus validating the global nonlinear proposed strategy.