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Research Papers

Vibration Response Characteristics of Quasi-Periodic Sandwich Beam With Magnetorheological Visco-Elastomer Core Under Random Support Excitations

[+] Author and Article Information
Z. G. Ying

Department of Mechanics,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou 310027, China

Y. Q. Ni

Department of Civil and
Environmental Engineering,
The Hong Kong Polytechnic University,
Kowloon, Hong Kong

R. H. Huan

Department of Mechanics,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou 310027, China
e-mail: rhhuan@zju.edu.cn

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 30, 2017; final manuscript received March 13, 2018; published online May 4, 2018. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 140(5), 051017 (May 04, 2018) (11 pages) Paper No: VIB-17-1347; doi: 10.1115/1.4039726 History: Received July 30, 2017; Revised March 13, 2018

The vibration control of a sandwich beam with supported mass subjected to random support motion excitations can be performed using magnetorheological visco-elastomer core with adjustable dynamic properties. The periodic distributions of geometrical and physical parameters of the sandwich beam can improve its vibration response characteristics. To further improve characteristics or reduce responses, the quasi-periodic sandwich beam with supported mass under random excitations is studied. The facial layer thickness and core layer modulus of the sandwich beam are considered as quasi-periodic distributions. The partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived and converted into ordinary differential equations for multi-degrees-of-freedom (DOFs) vibration. The expressions of frequency response and response spectral densities of the sandwich beam are obtained. Numerical results are given to illustrate the greatly improvable vibration response characteristics of the sandwich beam and the outstanding relative reduction localization of antiresonant responses. The proposed quasi-periodic distribution and analysis method can be used for the vibration control design of sandwich beams subjected to random excitations.

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Figures

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Fig. 1

Sandwich beam with MRVE core and supported mass

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Fig. 2

Perturbation (Δh1/h10) and periodic (h1p/h10) parts of facial layer thickness versus coordinate y

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Fig. 3

Logarithmic displacement responses of the sandwich beam versus frequency ω for different perturbation wave numbers k1ar of the thickness (har = 0.1b1m, k1r = 0)

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Fig. 4

Resonant and antiresonant frequency responses for different perturbation wave numbers k1ar: (a) first resonant response, (b) first antiresonant response, and (c) second antiresonant response

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Fig. 5

Relative displacement response changes versus frequency ω for different perturbation wave numbers k1ar of the thickness (har = 0.1b1m, k1r = 0)

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Fig. 6

Relative displacement response changes versus coordinate y for different frequencies (k1ar = 1.6, har = 0.1b1m, k1r = 0)

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Fig. 7

Logarithmic displacement response spectra of the sandwich beam for different perturbation wave numbers k1ar of the thickness (har = 0.1b1m, k1r = 0)

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Fig. 8

Logarithmic velocity response spectra of the sandwich beam for different perturbation wave numbers k1ar of the thickness (har = 0.1b1m, k1r = 0)

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Fig. 9

Logarithmic displacement responses of the sandwich beam versus frequency ω for different perturbation wave amplitudes har of the thickness (k1ar = 1.5, k1r = 0)

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Fig. 10

Relative displacement response changes versus coordinate y for different perturbation wave amplitudes har of the thickness (k1ar = 1.5, ω = 42Hz)

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Fig. 11

Logarithmic displacement responses of the sandwich beam versus frequency ω for different perturbation wave numbers k2ar of the modulus (Gar = 0.5b2m, k2r = 0)

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Fig. 12

Relative displacement response changes versus coordinate y for different frequencies (k2ar = 5.5, Gar = 0.5b2m, k2r = 0)

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Fig. 13

Logarithmic displacement responses of the sandwich beam versus frequency ω for different perturbation wave numbers k2pr of the modulus (Gpr = 0.1k2m, b2r = 0)

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Fig. 14

Relative displacement response changes versus frequency ω for different perturbation wave numbers k2pr of the modulus (Gpr = 0.1k2m, b2r = 0)

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Fig. 15

Logarithmic displacement responses of the sandwich beam versus frequency ω for different perturbation wave amplitudes Gpr of the modulus (k2pr = 2.0, b2r = 0)

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Fig. 16

Relative displacement response changes versus coordinate y for different perturbation wave amplitudes Gpr of the modulus (k2pr = 2.0, ω = 42Hz)

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