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Research Papers

Elastic–Viscoelastic Composite Structures Analysis With an Improved Burgers Model

[+] Author and Article Information
Shanhong Ren

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

Guozhong Zhao

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhaogz@dlut.edu.cn

Shunqi Zhang

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
School of Mechatronic Engineering
and Automation,
Shanghai University,
Shanghai 200444, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 21, 2017; final manuscript received January 1, 2018; published online January 25, 2018. Assoc. Editor: John Judge.

J. Vib. Acoust 140(3), 031006 (Jan 25, 2018) (10 pages) Paper No: VIB-17-1113; doi: 10.1115/1.4038906 History: Received March 21, 2017; Revised January 01, 2018

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.

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References

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Figures

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Fig. 2

The improved Burgers model

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Fig. 7

Two degrees-of-freedom mass–spring system

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Fig. 3

Comparison of the curve fitting results (real part)

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Fig. 4

Comparison of the curve fitting results (imaginary part)

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Fig. 5

Comparison of the curve fitting results (real part)

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Fig. 6

Comparison of the curve fitting results (imaginary part)

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Fig. 8

The composite beam with viscoelastic core

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Fig. 9

The finite element mesh of the quarter annular composite plate

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