Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

Zghal, Souhir; Bouazizi, Mohamed Lamjed; Bouhaddi, Noureddine

doi:10.1051/matecconf/20141608003

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…G 1 ðsÞ is considered as the Biot damping model and its parameters are chosen as given in Table 1. G 2 ðsÞ is considered as the GHM damping model and identified from material 242F01 3MTM by Zghal et al [63]. The parameters for GHM damping model are identified as α 1 ¼ 1:047, 1 ¼ 3911:89,ω 1 ¼ 4943:06 and G 0 ¼ 0:079 [63].…”

Section: Considering the Nonzero Initial Conditionsmentioning

confidence: 99%

Dynamics of structural systems with various frequency-dependent damping models

Deng

et al. 2015

Front. Mech. Eng.

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The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damping model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.

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Section: Considering the Nonzero Initial Conditionsmentioning

confidence: 99%

Dynamics of structural systems with various frequency-dependent damping models

Deng

et al. 2015

Front. Mech. Eng.

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“…They handled the viscoelastic core as complex layer and variant with frequency and temperature by using the Golla-Hughes-McTavish method to account for the frequency dependent properties of it. Zghal et al [7] gave an approach to deal with the local nonlinearities on the dynamic behavior of such model assembled structures. Finite element solutions are widely used for sandwich structures [8]- [12].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Uniform and Non-Uniform Cross-Section Cantilever Sandwich Beams

Hüseyinoğlu

ŞEN

Yiğid

et al. 2019

European Journal of Technic

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In this study, an analytical solution for dynamic analysis of uniform and nonuniform cross-section cantilever sandwich beam is presented. The sandwich beam was assumed to be an Euler-Bernoulli beam and formed with a thin core and two thin skin layers. So the shear deformations and rotational effects were neglected. The equivalent flexural rigidity was obtained for the entire sandwich structure. Some implementations for the solution method are given and the results are compared with numerical solutions. The usability of the Euler-Bernoulli Beam Theory for thin layered uniform or non-uniform sandwich beams is investigated. The solutions obtained from analytical and numerical solutions are in good agreement.

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“…However, many authors have found-out that the proposed mathematical models used for performing the frequency-and temperature-dependent behavior of viscoelastic materials, based on the concept of internal variables lead to global systems of equations of motion whose numbers of degrees of freedom (DOFs) largely exceed the order of the associated undamped structures (Balmès and Germès, 2002;de Lima et al, 2009;de Lima et al, 2010). As a result, if such response evaluations are made based on computations performed on the full finite element (FE) models of structures treated with viscoelastic materials composed by many thousands of DOFs, which is not rarely the case, the computational cost necessary to perform exact response evaluations during iterative processes such as structural optimization and uncertainty propagation, can become prohibitive, even unfeasible (de Lima et al, 2010;Zghal et al, 2014). Moreover, the increased dimension of the analytical models can preclude their use for active control and nonlinear vibration computations, in which time-domain analyses must be performed.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the proposed condensation strategies are restricted to the frequency-domain analysis, since the complex modulus approach is used to represent the viscoelastic dynamic features. More recently, Zghal et al (2014) have proposed a model reduction method of nonlinear dynamic analysis of viscoelastic systems in time domain using the well-known GollaHughes-McTavish (GHM) model (Golla and Hughes, 1985;McTavish and Hughes, 1993). However, it leads to augmented global systems of equations of motion whose numbers of DOFs largely exceed the order of the associated undamped structures.…”

Section: Introductionmentioning

confidence: 99%

A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems

Lima

Bouhaddi

Rade

et al. 2015

Lat. Am. j. solids struct.

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Many authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency-and temperaturedependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency-and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.

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Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

Cited by 3 publications

References 9 publications

Dynamics of structural systems with various frequency-dependent damping models

Dynamics of structural systems with various frequency-dependent damping models

Dynamic Analysis of Uniform and Non-Uniform Cross-Section Cantilever Sandwich Beams

A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems

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