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

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Experiments and simulations of the structure Harmony-Gamma subjected to broadband random vibrations - Modeling, numerical simulationsand experiments

International audienceThe structure Harmony-Gamma is a metallic assembly representative of an industrial structure for which the vibratory response is influenced by the apparition of nonlinear phenomena within two specific types of joints, the first corresponding to friction joints and the second to elastomer joints. The present study extends the previous work based on experiments and numerical simulations of the structure Harmony-Gamma subjected to harmonic vibrations [1]. More specifically, the nonlinear vibrational behaviour of the assembly subjected to random broadband excitations is studied. Broadband excitations are performed experimentally, in order to provide a first understanding of the nonlinear effect of both the friction and elastomer joints. Additionally, a global numerical methodology based on finite-element modelling and the use of the Harmonic Balance Method for the prediction of the nonlinear response of the Harmony-Gamma structure subjected to stochastic excitation is proposed. It is demonstrated that the use of a numerical model that has been validated against experimental tests can furthermore be used to achieve a refined understanding of the nonlinear phenomena and their origin

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

International audienceThis 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

Experiments and simulations of an industrial assembly with different types of nonlinear joints subjected to harmonic vibrations

International audienceThe structure Harmony-Gamma is a metallic assembly representative of an industrial structure for which the vibratory response is influenced by the apparition of nonlinear phenomena within two specific types of joints, the first corresponding to friction joints and the second to elastomer joints. Firstly, the paper presents the experimental procedure and results obtained for this structure. Secondly, a global methodology for modeling and simulation of the nonlinear vibrational response is set up. The experiments are performed for longitudinal and transverse swept sine experiments. First of all, swept sine experiments are performed at low excitation levels on the structure in order to update a linear finiteelement model. Then, the evolution of the frequency response function is studied at increasing excitation levels in order to identify the contribution of the nonlinear effects on the global vibrational response of the system. The methodology for modeling and simulation consists of five steps. Firstly, a finite-element model of the structure is presented and updated in order to be representative of the structure when it is excited at low excitation levels. This model is then reduced using a hybrid sub-structuring technique. Thirdly, the nonlinear models of the friction and elastomer joints are added. The resulting optimization problem is solved by means of the Harmonic Balance Method (HBM) coupled with a Newton-Raphson continuation and a condensation process. Lastly, the simulation results are compared to the experimental results in order to validate the development of the finite element model for the nonlinear industrial structure Harmony-Gamma with nonlinear joints of different natures and to achieve a refined understanding of the nonlinear phenomena and their origin

Experiments and nonlinear simulations of a rubber isolator subjected to harmonic and random vibrations

International audienceThis paper presents experiments and numerical simulations of a nonlinear rubber isolator subjected to both harmonic and broadband random excitations. Harmonic and broadband random excitations are performed experimentally in order to show the softening effect of the rubber isolator for high amplitudes of displacement and to show the temperature dependency of its mechanical properties. Firstly, the rubber isolator is modeled as a one degree-of-freedom system, whose stiffness and damping depend only on the amplitude of the relative displacement of the joint. The relationship between the stiffness and the damping versus the amplitude of the relative displacement of the rubber isolator is updated via experiments. Secondly, the Harmonic Balance Method (HBM) and the shooting method are presented and extended to take into account both harmonic and random excitations. A modification of the nonlinear methods is necessary in order to recover the information concerning the displacement amplitude. Moreover, for random excitations, a periodogram strategy is used to ensure a good estimate of the resulting Power Spectral Density (PSD). Finally, comparisons between experiments and simulations are undertaken. Good correlations are observed for harmonic and broadband random excitations, thus validating the modeling of the rubber isolator and the proposed nonlinear methodology

Dataset of measurements for the experimental CEA-beam benchmark structure subjected to one stochastic broadband excitation.

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