Non-linear vibrations of a beam with non-ideal boundary conditions and uncertainties – Modeling, numerical simulations and experiments

Abstract

This paper presents experiments and numerical simulations of a nonlinear clamped-clamped beam subjected to Harmonic excitations and epistemic uncertainties. These uncertainties are propagated in order to calculate the dynamic response of the nonlinear structure via a coupling between the Harmonic Balance Method (HBM) and a non-intrusive Polynomial Chaos Expansion (PCE). The system studied is a clampedclamped steel beam. First of all, increasing and decreasing swept sine experiments are performed in order to show the hardening effect in the vicinity of the primary resonance, and to extract the experimental multi-Harmonic frequency response of the structure. Secondly, the Harmonic Balance Method (HBM) is used alongside a continuation process to simulate the deterministic response of the nonlinear clamped-clamped beam. Good correlations were observed with the experiments, on the condition of updating the model for each excitation level. Finally, the effects of the epistemic uncertainties on the variability of the nonlinear response are investigated using a non-intrusive Polynomial Chaos Expansion (PCE) alongside the Harmonic Balance Method (HBM). A new methodology based on a phase criterion was developed in order to allow the PCE analysis to be performed despite the presence of bifurcations in the nonlinear response. The efficiency and robustness of the proposed methodology is demonstrated by comparison with Monte Carlo simulations. Then, the stochastic numerical results are shown to envelope the experimental responses for each excitation level without the need for model updating, validating the nonlinear stochastic methodology as a whole.

Effect of Friction on the Structural Dynamics of Built-Up Structures: An Experimental Study

“…Copyright © 2020 by ASME; reuse license CC-BY 4.0 cost. In addition, a significant amount of uncertainty is also introduced by the large number of nonlinear sources [24,25], mistuning [4,26,27], wear [13], manufacturing tolerances, mounting [10], etc. For all these reasons, the impact of friction joints on the dynamics becomes quite complicated to predict.…”

Simulation and Experimental Substantiation of Beam Deflection under Guided End Conditions

“…Numerical results are validated with experimental and finite element analysis results. Roncen [20] studied the nonlinear vibration of a clamped beam subjected to epistemic uncertainties and harmonic excitation. The consequences of the epistemic uncertainties on the dynamic response were explored using Harmonic Balance Method (HBM) and non-intrusive Polynomial Chaos Expansion (PCE).…”

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

“…The latter is based on a stochastic description of the uncertain parameters and comprises the projection of the random variable on a polynomial basis orthogonal with respect to the PDF. This approach has already proven its efficiency for the uncertainty propagation of linear and nonlinear FRFs [41][42][43]. The PCE has also been coupled with multi-harmonic balance methods to investigate the effects of the uncertainties in nonlinear systems [44,45].…”