A Finite Element Model for the Vibration Analysis of Sandwich Beam with Frequency-Dependent Viscoelastic Material Core
TL;DR: A finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest.
Abstract: In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.
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30 Sep 1986
TL;DR: In this paper, the authors used the canonical M, K form of the undamped motion equations to model viscoelastic damping and used finite element analysis to model the damping factors.
Abstract: Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.
339 citations
TL;DR: Athree-layer composite plate element is developed for finite element modeling and vibration analysis of sandwich plate with frequency-dependent viscoelastic material core and has certain reference and application value for solving similar engineering vibration problems.
Abstract: Athree-layer composite plate element is developed for finite element modeling and vibration analysis of sandwich plate with frequency-dependent viscoelastic material core. The plate element is quadrilateral element bounded by four-node with 7-degree-of-freedom per node. The frequency-dependent characteristics of viscoelastic material parameters are described using the Biot model. The method of identifying the parameters of the Biot model is given. By introducing auxiliary coordinates, the Biot model is combined with the finite element equation of the viscoelastic sandwich plate. Through a series of mathematical transformations, the equation is transformed into a standard second-order steady linear system equation form to simplify the solution process. Finally, the vibration characteristics of the viscoelastic sandwich plate are analyzed and experimentally studied. The results show that the method in this paper is correct and reliable, and it has certain reference and application value for solving similar engineering vibration problems.
7 citations
TL;DR: In this paper, a dynamic model of a sandwich beam with viscoelastic coating based on a fractional constitutive equation was developed, which is a generalized model of sandwich beams.
Abstract: In this study, a dynamic model of a sandwich beam with viscoelastic coating based on a fractional constitutive equation was developed. The fractional model is a generalized model of sandwich beams ...
7 citations
TL;DR: In this article, the kinematic assumption free and thermodynamically consistent formulation for bending of thermoelastic beams presented by Surana et al. was extended to the case of a single beam.
Abstract: The work presented in this paper extends the kinematic assumption free and thermodynamically consistent formulation for bending of thermoelastic beams presented by Surana et al. for bending of ther...
6 citations
TL;DR: In this paper, the free vibration model of a steel-polymer concrete beam based on Timoshenko beam theory is presented, which is characterized by high compliance with the experimental data: the relative error in the case of natural vibration frequencies does not exceed 0.4%, on average 0.2%.
Abstract: The free vibration model of a steel-polymer concrete beam based on Timoshenko beam theory is presented in this paper. The results obtained on the basis of the model analysis, describing values of the natural frequencies of the beam, were compared with the results obtained by the solution of the model formulated on the basis of the classical Euler-Bernoulli beam theory, the finite element model and the results of experimental studies. The developed model is characterized by high compliance with the experimental data: the relative error in the case of natural vibration frequencies does not exceed 0.4%, on average 0.2%.
6 citations
References
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TL;DR: In this article, the transverse displacement of a three-layer sandwich beam with a viscoelastic core is derived in terms of the transversal displacement, w, for a 3D beam.
785 citations
"A Finite Element Model for the Vibr..." refers background in this paper
...[7], DiTaranto [8], Mead and Markus [9] and Yan and Dowell [10]....
[...]
...Early works on the damping characteristics of the viscoelastic composite structures were carried out by Kerwin Jr. [7], DiTaranto [8], Mead and Markus [9] and Yan and Dowell [10]....
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...[7], DiTaranto [8], Mead and Ma kus [9] and Yan and Dowell [10]....
[...]
TL;DR: In this article, a quantitative analysis of the damping effectiveness of a constrained layer of damping tape is presented, where the loss factor η is defined as the normalized imaginary part of the complex bending stiffness of the damped plate.
Abstract: For a number of years it has been known that flexural vibrations in a plate can be damped by the application of a layer of damping (viscoelastic) material that is in turn constrained by a backing layer or foil. A common example is the damping tape currently used in aircraft.This paper presents a quantitative analysis of the damping effectiveness of such a constrained layer. As in the work of H. Oberst the damping is characterized by the loss factor η, which is the normalized imaginary part of the complex bending stiffness of the damped plate.The calculated damping factor depends on the wavelength of bending waves in the damped plate, and on the thicknesses and elastic moduli of the plate, the damping layer, and the constraining layer. A complex shear modulus is assigned to the damping layer, where all of the energy dissipation is assumed to take place.Damping factors have been determined experimentally on laboratory test bars for a number of constrained‐damping‐layer applications for frequencies from abou...
693 citations
"A Finite Element Model for the Vibr..." refers background in this paper
...[7], DiTaranto [8], Mead and Markus [9] and Yan and Dowell [10]....
[...]
...[7], DiTaranto [8], Mead and Ma kus [9] and Yan and Dowell [10]....
[...]
TL;DR: In this article, an efficient method for finite element modeling of three-layer laminates containing a viscoelastic layer is described, and modal damping ratios are estimated from undamped normal mode results by means of the modal strain energy method.
Abstract: An efficient method is described for finite element modelling of three-layer laminates containing a viscoelastic layer. Modal damping ratios are estimated from undamped normal mode results by means of the modal strain energy method. Comparisons are given between results obtained by the MSE method implemented in NASTRAN, by various exact solutions for approximate governing differential equations, and by experiment. Results are in terms of frequencies, modal damping ratios, and mechanical admittances for simple beams, plates, and rings. Application of the finite element -- MSE method in design of integrally damped structures is discussed.
542 citations
Book•
06 Jul 2001
TL;DR: In this article, the effects of temperature and frequency on complex modulus properties of Viscoelastic Materials are investigated. But the authors focus on the effect of temperature on complex modulation properties and do not consider the effect on the properties of simple Viscoellastic systems.
Abstract: Preface. Introduction to Damping. Modeling the Dynamic Mechanical Behaviour of Viscoelastic Materials. The Effects of Temperature and Frequency on Complex Modulus Properties. Measurement of Complex Modulus Properties. Numerical Analysis of Measured Complex Modulus Data. The Complex Modulus Behaviour of Typical Polymeric Materials. Harmonic and Non-harmonic Response of Simple Viscoelastic Systems. Controlling Vibration using Viscoelastic Materials. References. Symbols for Chapter 8. Selected Computer Programmes. Units and Dimensions. Author Index. Subject Index.
520 citations
509 citations
"A Finite Element Model for the Vibr..." refers background in this paper
...Early works on the damping characteristics of the viscoelastic composite structures were carried out by Kerwin Jr. [7], DiTaranto [8], Mead and Markus [9] and Yan and Dowell [10]....
[...]
...Early works on the damping characteristi s of the visco lastic composite structures were carried out by Kerwin Jr. [7], DiTaranto [8], Mead and Ma kus [9] and Yan and Dowell [10]....
[...]
...[7], DiTaranto [8], Mead and Ma kus [9] and Yan and Dowell [10]....
[...]
...[7], DiTaranto [8], Mead and Markus [9] and Yan and Dowell [10]....
[...]