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Guedri M.,Preparatory Engineering Institute of Nabeul IPEIN | Lima A.M.G.,Federal University of Itajuba | Bouhaddi N.,University of Franche Comte | Rade D.A.,Federal University of Uberlandia
Mechanical Systems and Signal Processing

In this paper, a methodology of uncertainty propagation is investigated as related to constrained viscoelastic layers in the context of passive vibration damping. The uncertainties are introduced on multilayer beam and plate finite elements by means of an original strategy, which consists in introducing the perturbations after an adequate parameterisation of the mass and complex stiffness matrices. Such parameterisation scheme enables to perform iterative model updating, sensitivity analyses and uncertainty propagation analyses at a moderate computational cost since re-actualisation of the nominal global finite element matrices is not required. The design space is composed by both the parameters characterising the viscoelastic treatment and those of the base structure. The theoretical foundations related to the modelling of viscoelastic systems and stochastic finite element models are first reviewed, followed by a description of the parameterisation technique. Finally, numerical applications are presented to demonstrate the effectiveness of the proposed strategy for the robust design of structures incorporating viscoelastic materials. Crown Copyright © 2009. Source

Guedri M.,Preparatory Engineering Institute of Nabeul IPEIN | Cogan S.,University of Franche Comte | Bouhaddi N.,University of Franche Comte
Mechanical Systems and Signal Processing

Methods for the robust design of mechanical systems have the objective to reduce the variability in system performance with respect to uncertainties in the material and geometrical properties of a mechanical structure as well as in its interactions with its environment. Two types of uncertainty are encountered in practice, namely aleatory and epistemic uncertainties. Aleatory uncertainty is generally considered to be irreducible and results from statistical variations in the physical properties of components and interfaces. Epistemic uncertainties are due to a lack of accurate knowledge concerning the physical laws governing the behavior of a component or interface and can generally be reduced with a combination of more detailed modeling and experimental investigations. Epistemic uncertainties can be difficult to characterize due to simplifications in geometric and material field properties, and as such are rarely taken into account explicitly in reliability analysis. In the present work, we propose to examine the robustness of a classical reliability analysis with respect to both aleatory and epistemic uncertainty. The latter will be represented using a non-parametric approach in order to avoid a detailed characterization of the lack of knowledge present in the system. This then allows us to study in detail how the results of the reliability analysis vary as a function of the degree of lack of knowledge. The proposed methodology is illustrated using numerical simulations. © 2011 Elsevier Ltd. All rights reserved. Source

Abed I.,University of Franche Comte | Abed I.,Tunis el Manar University | Kacem N.,University of Franche Comte | Bouhaddi N.,University of Franche Comte | And 2 more authors.
Smart Materials and Structures

We propose a multi-modal vibration energy harvesting approach based on arrays of coupled levitated magnets. The equations of motion which include the magnetic nonlinearity and the electromagnetic damping are solved using the harmonic balance method coupled with the asymptotic numerical method. A multi-objective optimization procedure is introduced and performed using a non-dominated sorting genetic algorithm for the cases of small magnet arrays in order to select the optimal solutions in term of performances by bringing the eigenmodes close to each other in terms of frequencies and amplitudes. Thanks to the nonlinear coupling and the modal interactions even for only three coupled magnets, the proposed method enable harvesting the vibration energy in the operating frequency range of 4.6-4.5 Hz, with a bandwidth of 190% and a normalized power of 20.2 mW cm-3 g-2. © 2016 IOP Publishing Ltd. Source

Ghanmi S.,Preparatory Engineering Institute of Nabeul IPEIN | Guedri M.,Preparatory Engineering Institute of Nabeul IPEIN | Bouazizi M.-L.,Preparatory Engineering Institute of Nabeul IPEIN | Bouhaddi N.,University of Franche Comte
Mechanical Systems and Signal Processing

This paper presents a new approach to robust multi-objective and multi-level optimization of the design of complex mechanical structures. The optimization is at two levels: system and elements. At system-level, the robust multi-objective problem has four cost functions: on the one hand the minimization of the global mass and displacement at a fixed point of the mechanical structure, and on the other hand the maximization of both the robustness and the displacement of the mass. At element-level the robust multi-objective problem has two cost functions: minimization of the element mass and maximization of its robustness. A robust condensation technique, based on an enriched KarhunenLoève condensation, is used for complex structures which require a large finite element model. In contrast to existing formulations, this new approach takes into account uncertainties in the design parameters at system-level and element-level. It also allows for the task sharing which is commonly used in structural engineering. © 2010 Elsevier Ltd. All rights reserved. Source

Rabhi N.,Preparatory Engineering Institute of Nabeul IPEIN | Guedri M.,Preparatory Engineering Institute of Nabeul IPEIN | Hassis H.,National Engineering School of Tunis | Bouhaddi N.,University of Franche Comte
Mechanical Systems and Signal Processing

Mathematical modeling of physical systems is essential to understand and, if possible, control such systems. However, insufficient information may be available about the level of uncertainty related to material properties, geometric parameters, boundary conditions and the applied loads. In the context of structural reliability, the uncertainties may be uncontrollable when designing for robustness. These problems in the modeling of the uncertainties are often complicated by the models inability to describe the physical phenomena that are involved. In this paper, the proposed approach combines a dynamic reliability method and a meta-model (reduced model) to obtain good results in terms of the reliability and optimization of such systems. Using the available information about the uncertain design parameters, we use the hybrid model coupling of the possibility and probability approaches for the propagation of the uncertainties in the model. The proposed method was implemented on theoretical structures with different meta-models. The results are compared with the Monte Carlo simulations. This allowed us to prove the robustness and efficiency of the proposed methodology for reliability calculations of complex dynamic structures. © 2010 Elsevier Ltd. All rights reserved. Source

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