Research Papers

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

[+] Author and Article Information
Y. Y. Chen

Department of Systems Engineering,
University of Arkansas at Little Rock,
Little Rock, AR 72204

G. L. Huang

Department of Systems Engineering,
University of Arkansas at Little Rock,
Little Rock, AR 72204
e-mail: glhuang@ualr.edu

C. T. Sun

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: sun@purdue.edu

1Present address: Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, MO 65211.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 12, 2013; final manuscript received July 31, 2014; published online September 11, 2014. Assoc. Editor: Jiong Tang.

J. Vib. Acoust 136(6), 061008 (Sep 11, 2014) (8 pages) Paper No: VIB-13-1359; doi: 10.1115/1.4028378 History: Received October 12, 2013; Revised July 31, 2014

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

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Fig. 1

Principle of operation of the negative capacitance circuit A, (a) piezoelectric sample disconnect from the circuit and (b) piezoelectric sample connected with the circuit

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Fig. 2

(a) Piezoelectric patch connected to a parallel negative capacitance −Cn and (b) equivalent piezoelectric patch

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Fig. 3

Normalized effective modulus of piezoelectric patch with different NCRs in circuits A and B, respectively

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Fig. 4

Active mass-in-mass lattice system with inner spring to represent negative capacitance piezoelectric shunting

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Fig. 5

Band gap of the active mass-in-mass lattice system with different NCRs, (a) λ = 0, (b) λ = −0.80, (c) λ = −0.84, (d) λ = −0.90, (e) λ = −1.00, and (f) λ = −1.50

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Fig. 6

Displacement amplitude ratio U2/U1 of the inner mass m2 to the outer mass m1

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Fig. 7

Band gap variations of the active mass-in-mass lattice system with different NCRs (bond should be bound)

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Fig. 8

(a) Active elastic metamaterial plate with a periodic array of the cantilever-mass system bonded by shunted piezoelectric patches and (b) detailed microstructure in the unit cell

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Fig. 9

Band gap variation of the active elastic metamaterial plate with different NCRs for in-plane longitudinal wave, (a) λ = 0, (b) λ = −0.842, (c) λ = −0.846, (d) λ = −0.863, (e) λ = −0.8585, and (f) λ = −0.858

Grahic Jump Location
Fig. 10

Band gap variation of the active elastic metamaterial plate with different NCRs for out-of-plane bending wave, (a) λ = 0, (b) λ = −0.83, (c) λ = −0.842, (d) λ = −0.898, (e) λ = −0.88, and (f) λ = −0.8775




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