Lamrhari, M. and Sarsri, D. and Azrar, L. and Rahmoune, M. and Sbai, K. (2016) Finite element reduced order models for nonlinear vibrations of large systems with uncertain parameters. In: UNSPECIFIED.

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This paper presents a finite element reduced order model for the nonlinear vibrations of large structured mechanics system with uncertain parameters. In this model, the reduced-order formulation of the discredited problem is obtained by expanding the mechanical displacement unknown vector onto the Eigen mode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. The methods are designed to predict dynamic behavior of structures liable to minor changes in physical and geometrical properties. The methods combine stochastic Finite Element Methods (FEM) with the specific class of modal reduction known as Component Mode Synthesis (CMS). The CMS gives the possibility to use sub-structuring. The most basic way of achieving this goal, is by running several dynamic analyses over and over, each with slightly varied input parameters. Using all separate response results as input for a statistic analysis results in an estimation of the overall response, and the sensitivity of this response to the varied parameters. This method is known as Monte Carlo Simulation (MCS). It is very time consuming, since for every variation of parameters a total FEM-analysis has to be performed. To reduce this calculation time, perturbation methods will be used and model reduction will be applied, to obtain the stochastic system response. The numerical method of Newmark's used for direct integration of differential non linear equations of motion describing systems; the statistical moments (mean, variance) of dynamic response of the reduced system are obtained by the second order perturbation method. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures for large FE models with uncertain parameters are presented.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Uncontrolled Keywords: Dynamic analysis; Dynamics; Equations of motion; Intelligent systems; Modal analysis; Monte Carlo methods; Nonlinear analysis; Numerical methods; Perturbation techniques; Stochastic models; Stochastic systems; Structural analysis; Uncertainty analysis, Component mode synthesis; Geometrical property; Mechanical displacements; Non-linear vibrations; Second order perturbation; Stochastic finite element method; Uncertain parameters; Variation of Parameters, Finite element method
Subjects: Engineering
Divisions: SCIENTIFIC PRODUCTION > Engineering
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:47

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