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Research Papers

Integer and Fractional Order-Based Viscoelastic Constitutive Modeling to Predict the Frequency and Magnetic Field-Induced Properties of Magnetorheological Elastomer

[+] Author and Article Information
Umanath R. Poojary

Department of Mechanical Engineering,
National Institute of Technology Karnataka,
Surathkal 575025, Mangalore, India
e-mail: umanr@hotmail.com

K. V. Gangadharan

Professor
Department of Mechanical Engineering,
National Institute of Technology Karnataka,
Surathkal 575025, Mangalore, India
e-mail: kvganga@nitk.ac.in

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 22, 2017; final manuscript received January 17, 2018; published online February 23, 2018. Assoc. Editor: Alper Erturk.

J. Vib. Acoust 140(4), 041007 (Feb 23, 2018) (15 pages) Paper No: VIB-17-1333; doi: 10.1115/1.4039242 History: Received July 22, 2017; Revised January 17, 2018

Magnetorheological elastomer (MRE)-based semi-active vibration mitigation device demands a mathematical representation of its smart characteristics. To model the material behavior over broadband frequency, the simplicity of the mathematical formulation is very important. Material modeling of MRE involves the theory of viscoelasticity, which describes the properties intermediate between the solid and the liquid. In the present study, viscoelastic property of MRE is modeled by an integer and fractional order derivative approaches. Integer order-based model comprises of six parameters, and the fraction order model is represented by five parameters. The parameters of the model are identified by minimizing the error between the response from the model and the dynamic compression test data. Performance of the model is evaluated with respect to the optimized parameters estimated at different sets of regularly spaced arbitrary input frequencies. A linear and quadratic interpolation function is chosen to generalize the variation of parameters with respect to the magnetic field and frequency. The predicted response from the model revealed that the fractional order model describes the properties of MRE in a simplest form with reduced number of parameters. This model has a greater control over the real and imaginary part of the complex stiffness, which facilitates in choosing a better interpolating function to improve the accuracy. Furthermore, it is confirmed that the realistic assessment on the performance of a model is based on its ability to reproduce the results obtained from optimized parameters.

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Figures

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Fig. 2

(a) Schematic representation of dynamic property measurement experimental setup and (b) actual image of the dynamic compression property measurement apparatus

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Fig. 1

(a) 3D image of test fixture for the dynamic compression test, (b) mode shape of test fixture corresponding to the fundamental frequency, (c) contour plots of the magnetic field, (d) magnetic field variation along the diameter of the MRE sample, and (e) magnetic field variation along the distance between the magnets

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Fig. 5

(a) Two-Maxwell MRE model, (b) fractional Maxwell MRE model, (c) geometry of two particles of diameter a within a particle chain, and (d) magnetic interaction between two particles approximated as dipole moments m shared with respect to one another

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Fig. 3

(a)–(d) Magnetic field-dependent variation in the hysteresis loop for 8 Hz, 12 Hz, 16 Hz, and 20 Hz

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Fig. 4

(a) and (b) Magnetic field and frequency-dependent variation in K* and C of MRE

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Fig. 7

(a)–(f) Variation in the parameters of two-Maxwell model with respect to B and f corresponding to three point input

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Fig. 8

(a)–(f) Variation in the parameters of two-Maxwell model with respect to B and f corresponding to five point input

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Fig. 6

(a) and (b) Force-displacement hysteresis loop corresponding to experimental and fitted data for 8 Hz and 16 Hz at 0 T and 0.27 T

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Fig. 9

(a)–(e) Variation in the parameters of fractional Maxwell model with respect to B and f corresponding to three point input

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Fig. 10

(a)–(e) Variation in the parameters of fractional Maxwell model with respect to B and f corresponding to five point input

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Fig. 11

Comparison between the experimental and predicated K′ by two-Maxwell and fractional Maxwell model with different set of input at 0 T, 0.1 T, 0.2 T, and 0.27 T

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Fig. 12

Comparison between the experimental and predicated K″ by two-Maxwell and fractional Maxwell model with different set of input at 0 T, 0.1 T, 0.2 T, and 0.27 T

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Fig. 13

Percentage error in estimating K″ by two Maxwell and fractional Maxwell model at 0 T, 0.1 T, 0.2 T, and0.27T

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