Uncertainty propagation for nonlinear vibrations: A non-intrusive approach

Panunzio, Alfonso M.; Salles, Loïc; Schwingshackl, Christoph W.

doi:10.1016/j.jsv.2016.09.020

Cited by 22 publications

(9 citation statements)

References 23 publications

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“…Corresponding to this kind of random variable, the orthogonal polynomial 42–46 is chosen as the second kind Chebyshev polynomial. They are presented by Hi(ξ), i=0,1,2,… .…”

Section: Orthogonal Polynomial Approximationmentioning

confidence: 99%

“…Based on the Karhunen-Loe`ve expansion, Sepahvand and Marburg 41 explored the uncertainty quantification in structural dynamic problems with spatially random variation in material properties inducing uncertain stiffness and damping parameters of a mechanical resonator. Panunzio et al 42 used a combined method based on the stochastic methods with an asymptotic numerical method for predicting the influence of uncertain input uncertainties on dynamic behaviors of the nonlinear dynamic system. Li et al 43 presented an improved interval extension based on the second-order Taylor's series to analyze the influence of uncertain excitation conditions on performance of nonlinear monostable energy harvesters. Nonlinear energy resonators are inevitably affected by uncertain factors.…”

Section: Introductionmentioning

confidence: 99%

“…Panunzio et al. 42 used a combined method based on the stochastic methods with an asymptotic numerical method for predicting the influence of uncertain input uncertainties on dynamic behaviors of the nonlinear dynamic system. Li et al.…”

Section: Introductionmentioning

confidence: 99%

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Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

Huang

Zhou

Han

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, the Chebyshev polynomial approximation is firstly utilized to analyze the dynamical characteristics of the nonlinear vibration energy harvester with an uncertain parameter. First, the stochastic energy harvester is transformed into a high-dimensional equivalent deterministic system by the Chebyshev polynomial approximation. And the ensemble mean response of the stochastic energy harvester is introduced to discuss the stochastic response. Then, the effectiveness of the approximation method is verified by numerical results. Furthermore, the bifurcation property of the displacement and voltage is analyzed, which is also consistent with the results derived by the top Lyapunov exponent. It is found that random factor can induce the appearance of multi-periodic phenomena and lead to appear the behavior of the periodic bifurcation. The strong random factor induces the fluctuation of the output voltage. In addition, the existence of the random factor greatly influences the property of the sub-harmonics and super-harmonics of the spectrum. Overall, the response mechanism of the nonlinear vibration energy harvester with an uncertain parameter is revealed.

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“…Corresponding to this kind of random variable, the orthogonal polynomial 42–46 is chosen as the second kind Chebyshev polynomial. They are presented by Hi(ξ), i=0,1,2,… .…”

Section: Orthogonal Polynomial Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

Huang

Zhou

Han

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…This leads to spurious oscillations, called the Gibbs phenomenon, which deteriorate the quality of the frequency response functions. These two problems have been encountered and dealt with in a recent article by Panunzio et al [29]. They used an Asymptotic Numerical Method (ANM, see [30] for details) coupled with an NIPCE for a Duffing oscillator.…”

Section: Linking Of the Hbm And The Nipcmentioning

confidence: 99%

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

Roncen

Sinou

Lambelin

2018

Mechanical Systems and Signal Processing

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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.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Yuan

Fantetti

Denimal

et al. 2021

Mechanical Systems and Signal Processing

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Underplatform dampers are widely used in turbomachinery to mitigate structural vibrations by means of friction dissipation at the interfaces. The modelling of such friction dissipation is challenging because of the high variability observed in experimental measurements of contact parameters. Although this variability is not commonly accounted for in state-of-the-art numerical solvers, probabilistic approaches can be implemented to include it in dynamics simulations in order to significantly improve the estimation of the damper performance. The aim of this work is to obtain uncertainty bands in the dynamic response of turbine blades equipped with dampers by including the variability observed in interfacial contact parameters. This variability is experimentally quantified from a friction rig and used to generate uncertainty bands by combining a deterministic state-of-the-art numerical solver with stochastic Polynomial Chaos Expansion (PCE) models. The bands thus obtained are validated against experimental data from an underplatform damper test rig. In addition, the PCEs are also employed to perform a variance-based global sensitivity analysis to quantify the influence of contact parameters on the variation in the nonlinear dynamic response via Sobol indices. The analysis highlights that the influence of each contact parameter in vibration amplitude strongly varies over the frequency range, and that Sobol indices can be effectively used to analyse uncertainties associated to structures with friction interfaces providing valuable insights into the physics of such complex nonlinear systems.

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Uncertainty propagation for nonlinear vibrations: A non-intrusive approach

Cited by 22 publications

References 23 publications

Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

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

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

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