A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures

Daya, El Mostafa; Potier‐Ferry, Michel

doi:10.1016/s0045-7949(00)00151-6

Cited by 165 publications

(114 citation statements)

References 18 publications

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“…The strategy for the solution of viscoelastic beam is described in [5] and employs the Newton-Raphson method with initial values being the natural frequency and the eigenshape of the chosen mode obtained for a purely elastic beam. Thus in the first step we find the natural frequencies and eigenshapes for the beam with the real ω-independent part of the global stiffness matrix K g,∞ , i.e.…”

Section: Dynamic Analysismentioning

confidence: 99%

Finite element models for laminated glass units with viscoelastic interlayer for dynamic analysis

Janda¹,

Zemanová²,

Zeman³

et al. 2016

WIT Transactions on the Built Environment

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In this contribution, a methodology for calibration and validation of a finite element model for dynamic response of laminated glass units with viscoelastic interlayer is proposed. The model is based on a refined theory in which the adjacent layers are connected by kinematic constrains ensuring the inter-layer compatibility. The time-dependent behavior of the interlayer is accounted for by the generalized Maxwell model. The resulting system is solved by the Newton method with consistent linearization and allows for quantification of natural frequencies and eigenshapes. The calibration of the generalized Maxwell chain exploits the experimental master curve obtained from the rheometer test while the analysis of the dynamic response of glass beam serves for model validation.

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Section: Dynamic Analysismentioning

confidence: 99%

Finite element models for laminated glass units with viscoelastic interlayer for dynamic analysis

Janda¹,

Zemanová²,

Zeman³

et al. 2016

WIT Transactions on the Built Environment

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“…To comply with this need, various procedures can be adopted regarding the computation of the reduction basis: (i) one can simply neglect this dependence by considering the stiffness matrix as being constant (Balmès and Germès, 2002). In this case, the reduction basis is also constant; (ii) one can use a constant reduction basis obtained by the resolution of the nonlinear eigenvalue problem associated to a frequency-and temperature-dependent stiffness matrix (Palmeri and Ricciardelli, 2006;Daya and Potier-Ferry, 2001;Plouin and Balmès, 1998); (iii) one can use an iterative method for the re-actualization of the basis according to frequency and temperature (Balmès and Germès, 2002). In this work, the strategy proposed consists in using a reduction basis formed by a constant modal basis of the associate conservative system.…”

Section: Robust Condensation Of Viscoelastic Systemsmentioning

confidence: 99%

Optimization of viscoelastic systems combining robust condensation and metamodeling

Lima¹,

Rade²,

Bouhaddi³

2010

J. Braz. Soc. Mech. Sci. & Eng.

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Passive control is recognized as being advantageous in terms of stability, effectiveness in broader bandwidths and ease of implementation (Nashif et al., 1985). In particular, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications, where they can be applied either as discrete devices or surface treatments at a relatively low cost (Samali and Kwok, 1995;Rao, 2001;de Lima et al., 2009; Espíndola et al., 2005). However, viscoelastic materials present some inherent drawbacks such as the influence of operational and environmental factors (frequency, temperature, pre-loads, moisture, etc.). Also, viscoelastic damping systems (specially, surface treatments) are prone to induce considerable mass additions. This last feature leads to the necessity of performing optimization aiming at achieving the desired performance and, at the same time, complying with design and construction constraints.In the last decades, much effort has been devoted to the development of finite element (FE) models capable of accounting for the typical dependence of the viscoelastic behavior with respect to frequency and temperature (Bagley and Torvik, 1983;MacTavish and Hughes, 1993;Lesieutre and Lee, 1996;Galucio et al., 2004). As a result, it is currently possible to model complex real-world engineering structures such as automobiles, airplanes, communication satellites, buildings and space structures (Balmès and Germès, 2002). A natural extension of this modeling capability is the optimization of the viscoelastic devices aiming the reduction of cost and/or the maximization of performance (Hao et al., 2004;Lee et al., 2004). In the quest for optimization, engineers are frequently faced with conflicting objectives. Such situations are conveniently dealt with by the so-called multiobjective or multicriteria optimization approach (Eschenauer et al., 1990). However, multiobjective optimization generally requires a large number of evaluations of the cost functions involved. For large finite element models of viscoelastic systems, typically composed of many thousands of degrees-of-freedom (DOFs), if such evaluations are made based on exact response computations performed on the full FE matrices, computation times can become prohibitive.The work reported herein intends to propose a general strategy for the reduction of the computational burden involved in the optimization of viscoelastic structures by combining Multiobjective Evolutionary Algorithms (MOEAs), robust condensation and Artificial Neural Networks (ANNs). The motivation for the use of (2002) and Masson et al. (2003), which is based on the use of an enriched modal basis for approximate model reduction. A so-named robust basis is constructed to take into account the structural modifications introduced by the inclusion of the viscoelastic treatments into the original system in such a way that updating of the reduction basis by exact re-analysis is avoided, leading to a drastic reduction of the time required to evaluate the cost fun...

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“…Researchers have considered different approaches to study these problems. Daya and Potier-Ferry [4] proposed a numerical method for the solution of nonlinear eigenvalue problems. This method associates homotopy and asymptotic numerical techniques and it was applied to the calculation of the natural frequencies and the loss factors of viscoelastically damped sandwich structures.…”

Section: Introductionmentioning

confidence: 99%

“…The reason why these theories were chosen is related to its less computational cost when compared to other higher order theories without loss of performance quality. As the inner layer of these structures is considered to behave in a viscoelastic way, the corresponding elastic properties are modelled using the complex method as some researchers [4,5,8] have also considered. The resulting dynamic problem is then solved in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of Soft Core Sandwich Beams with Metal-Graphene Nanocomposite Skins

Loja

2017

Shock and Vibration

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Sandwich structures are able to provide enhanced strength, stiffness, and lightweight characteristics, thus contributing to an improved overall structural response. To this sandwich configuration one may associate through-thickness graded core material properties and homogeneous or graded properties nanocomposite skins. These tailor-made possibilities may provide alternative design solutions to specific problem requisites. This work aims to address these possibilities, considering to this purpose a package of three beam layerwise models based on different shear deformation theories, implemented through Kriging-based finite elements. The viscoelastic behaviour of the sandwich core is modelled using the complex method and the dynamic problem is solved in the frequency domain. A set of case studies illustrates the performance of the models.

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A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures

Cited by 165 publications

References 18 publications

Finite element models for laminated glass units with viscoelastic interlayer for dynamic analysis

Finite element models for laminated glass units with viscoelastic interlayer for dynamic analysis

Optimization of viscoelastic systems combining robust condensation and metamodeling

Dynamic Response of Soft Core Sandwich Beams with Metal-Graphene Nanocomposite Skins

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