Khaoula Chikhaoui, Noureddine Bouhaddi, Najib Kacem, Mohamed Guedri and Mohamed Soula
The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and…
Abstract
Purpose
The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy.
Design/methodology/approach
The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel.
Findings
Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method.
Originality/value
The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.
Details
Keywords
Ramzi Lajili, Olivier Bareille, Mohamed Lamjed Bouazizi, Mohamed Ichchou and Noureddine Bouhaddi
This paper aims to propose numerical-based and experiment-based identification processes, accounting for uncertainties to identify structural parameters, in a wave propagation…
Abstract
Purpose
This paper aims to propose numerical-based and experiment-based identification processes, accounting for uncertainties to identify structural parameters, in a wave propagation framework.
Design/methodology/approach
A variant of the inhomogeneous wave correlation (IWC) method is proposed. It consists on identifying the propagation parameters, such as the wavenumber and the wave attenuation, from the frequency response functions. The latters can be computed numerically or experimentally. The identification process is thus called numerical-based or experiment-based, respectively. The proposed variant of the IWC method is then combined with the Latin hypercube sampling method for uncertainty propagation. Stochastic processes are consequently proposed allowing more realistic identification.
Findings
The proposed variant of the IWC method permits to identify accurately the propagation parameters of isotropic and composite beams, whatever the type of the identification process in which it is included: numerical-based or experiment-based. Its efficiency is proved with respect to an analytical model and the Mc Daniel method, considered as reference. The application of the stochastic identification processes shows good agreement between simulation and experiment-based results and that all identified parameters are affected by uncertainties, except damping.
Originality/value
The proposed variant of the IWC method is an accurate alternative for structural identification on wide frequency ranges. Numerical-based identification process can reduce experiments’ cost without significant loss of accuracy. Statistical investigations of the randomness of identified parameters illustrate the robustness of identification against uncertainties.
Details
Keywords
Mohamed Amine Ben Souf, Mohamed Ichchou, Olivier Bareille, Noureddine Bouhaddi and Mohamed Haddar
– The purpose of this paper is to develop a new formulation using spectral approach, which can predict the wave behavior to uncertain parameters in mid and high frequencies.
Abstract
Purpose
The purpose of this paper is to develop a new formulation using spectral approach, which can predict the wave behavior to uncertain parameters in mid and high frequencies.
Design/methodology/approach
The work presented is based on a hybridization of a spectral method called the “wave finite element (WFE)” method and a non-intrusive probabilistic approach called the “polynomial chaos expansion (PCE).” The WFE formulation for coupled structures is detailed in this paper. The direct connection with the conventional finite element method allows to identify the diffusion relation for a straight waveguide containing a mechanical or geometric discontinuity. Knowing that the uncertainties play a fundamental role in mid and high frequencies, the PCE is applied to identify uncertainty propagation in periodic structures with periodic uncertain parameters. The approach proposed allows the evaluation of the dispersion of kinematic and energetic parameters.
Findings
The authors have found that even though this approach was originally designed to deal with uncertainty propagation in structures it can be competitive with its low time consumption. The Latin Hypercube Sampling (LHS) is also employed to minimize CPU time.
Originality/value
The approach proposed is quite new and very simple to apply to any periodic structures containing variabilities in its mechanical parameters. The Stochastic Wave Finite Element can predict the dynamic behavior from wave sensitivity of any uncertain media. The approach presented is validated for two different cases: coupled waveguides with and without section modes. The presented results are verified vs Monte Carlo simulations.