Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams

Silva, V.A.C.; Lima, Antônio Marcos Gonçalves de; Bouhaddi, Noureddine; Lacerda, Helder Barbieri

doi:10.1016/j.ymssp.2019.07.022

Cited by 13 publications

(4 citation statements)

References 33 publications

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“…In [348], the authors analyzed the dynamic characteristics of a three-layered structure with a VE layer described by a fractional model. In the study [349], an iterative method was proposed to reduce the non-linear eigenvalue problem that arose after considering uncertainties, aiming to approximate complex eigenmodes. The authors studied a sandwich beam with a VE layer.…”

Section: Methods Of Sensitivity and Uncertainty Analysis Of Structure...mentioning

confidence: 99%

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Lewandowski,

Litewka,

Łasecka-Plura

et al. 2023

Buildings

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The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

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Section: Methods Of Sensitivity and Uncertainty Analysis Of Structure...mentioning

confidence: 99%

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Lewandowski,

Litewka,

Łasecka-Plura

et al. 2023

Buildings

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“…In order to solve Eq. (12) in the time-domain, the Newmark integration method [2,8,25] has been implemented, where the states X , Ẋ and Ẍ of the system at an iteration, i, for a given HCL sample, θ, are approximated by the following expressions:…”

Section: Stochastic Fe Modeling Of the Nonlinear Systemmentioning

confidence: 99%

“…Silva et al [2] have pointed out that, the structures' modernization, as well as the considerable increase of velocity in machine equipment's operation, contribute significantly to the occurrence of nonlinear phenomenon, characterized for disproportionality between cause and effect on the systems, which were not considered so far (only linear was considered). Thus, developing studies on vibrations in engineering structures is clearly important.…”

Section: Introductionmentioning

confidence: 99%

An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

Belonsi

Lima

Trevilato

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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The dynamic analysis of systems has several applications in the project or monitoring and controlling machines and equipments. In particular, the analysis of nonlinear systems has academic and industrial appeal for owning many particularities such as structural integrity, models updating, stability and real-time predictability. Those particularities complicate the study of these models. However, the development of more representative mathematical models requires normally costly computations. By considering the uncertainties associated with the fabrication process (geometrical dimensions, physical and material properties), as well as those related to the operational conditions (boundary conditions, external forces, etc.), it complicates further the analysis of those nonlinear systems. Thus, this paper proposes a methodology to analyze nonlinear systems subjected to uncertainties using the stochastic finite element method. In view of the high computational cost needed to construct the confidence region predicted with the stochastic nonlinear computational model, it is proposed herein a new model reduction method based on the construction of an adaptive iterative enriched basis to deal with the stochastic nonlinear system addressed herein composed by a thin rectangular plate used as an application. The results demonstrate clearly the efficiency and accuracy of the proposed method as an efficient tool to approximate the nonlinear responses of more complex nonlinear systems subjected to uncertainties. Also, it demonstrates the relevance of taking into account the uncertainties in the modeling of nonlinear systems to consider more realistic situations.

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“…As a result, much effort has been devoted to the development of accurate finite element (FE) models capable of predicting the linear behavior of structures containing viscoelastic materials for the purposes of vibration attenuation (Nashif et al, 1985). However, in more realistic applications of thin CVLs, due to the frequent occurrence of large displacements, the vibrations induced by the geometric nonlinearities differ significantly from those of linear approaches (Jacques et al, 2010; Silva et al, 2019) and a nonlinear modeling is found to be necessary.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty propagation and numerical evaluation of viscoelastic sandwich plates having nonlinear behavior

Silva

Lima

Ribeiro

et al. 2019

Journal of Vibration and Control

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The dynamic analysis of nonlinear viscoelastic systems in the frequency domain is not an easy task. In most cases, it is due to the frequency- and temperature-dependent properties of the viscoelastic part. Additionally, due to the inherent uncertainties affecting the viscoelastic efficiency in practical situations, their handling in the nonlinear modeling methodology becomes essential nowadays. However, it is still an issue. Thus, this paper presents a numerical modeling methodology intended to perform dynamic analyses in the frequency domain of thin sandwich plates under large displacements. The uncertainties characterizing the nonlinear dynamics of the viscoelastic system are introduced on the random linear and nonlinear finite element matrices by performing the Karhunen–Loève expansion technique. The Latin hypercube sampling method is used herein as the stochastic solver, and the nonlinear frequency responses are computed using the harmonic balance method combined with the Galerkin bases. To overcome the difficulty in solving the resulting complex nonlinear eigenproblem with a frequency-dependent viscoelastic stiffness, making the stochastic nonlinear analyses in the frequency domain very costly, sometimes unfeasible, an efficient and accurate iterative reduction method is proposed to approximate the complex eigenmodes. The envelopes of nonlinear frequency responses demonstrate clearly the relevance of considering the uncertainties in design variables of viscoelastic systems having nonlinear behavior to deal with more realistic situations.

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Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams

Cited by 13 publications

References 33 publications

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

Uncertainty propagation and numerical evaluation of viscoelastic sandwich plates having nonlinear behavior

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