Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance

Anton A. Kutsenko; Alexander L. Shuvalov; Olivier Poncelet; Alexander N. Darinskii

doi:10.1016/j.crme.2015.07.005

Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance

Anton A. Kutsenko ^1,²; Alexander L. Shuvalov ^1,²; Olivier Poncelet ^1,² ; Alexander N. Darinskii ³

¹ Univ. Bordeaux, I2M-APY, UMR 5295, 33405 Talence, France
² CNRS, I2M-APY, UMR 5295, 33405 Talence, France
³ Institute of Crystallography RAS, 119333 Moscow, Russia

Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 680-688.

Abstract

Normal propagation of the longitudinal wave through the piezoelectric medium with periodically embedded electrodes is considered. Each pair of electrodes is connected via a circuit with capacitance C. The paper analyzes in detail the unusual features of the dispersion spectrum $ω (K T)$ (K is the Floquet–Bloch wavenumber, T is the period) arising in the special case of a negative value of C. The solution of the dispersion equation shows explicitly the evolution of the passbands and stopbands tunable by varying $C < 0$ . One of the striking features is the existence of the poles of ImKT (infinite attenuation) and of the corresponding jumps of the phase ReKT from 0 to π in the stopbands for a certain range $(C_{0}, C_{1})$ of negative C. Besides, for $C \in (C_{0}, C_{\infty})$ where $C_{\infty} < C_{1}$ , the spectrum possesses a low-frequency absolute stopband starting from the quasistatic limit $ω = 0$ and including the tunable pole of ImKT inside. This stopband is related to the negative value of the quasistatic effective elastic constant in the range $(C_{0}, C_{\infty})$ . At $C = C_{\infty}$ , the effective constant is infinite while the spectrum degenerates to the straight line $K = 0$ at any ω. For C close to $C_{\infty}$ , the spectrum consists of the branches with high group velocity and of the quasiflat branches.

Received: 2015-03-24
Accepted: 2015-07-09
Published online: 2015-08-17

DOI: 10.1016/j.crme.2015.07.005

Keywords: Tunable phononic crystals, Piezoelectric structures, Electric control, Negative capacitance, Quasistatic stopband

Author's affiliations:

Anton A. Kutsenko ^{1, 2}; Alexander L. Shuvalov ^{1, 2}; Olivier Poncelet ^{1, 2}; Alexander N. Darinskii ³

¹ Univ. Bordeaux, I2M-APY, UMR 5295, 33405 Talence, France
² CNRS, I2M-APY, UMR 5295, 33405 Talence, France
³ Institute of Crystallography RAS, 119333 Moscow, Russia

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     author = {Anton A. Kutsenko and Alexander L. Shuvalov and Olivier Poncelet and Alexander N. Darinskii},
     title = {Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {680--688},
     publisher = {Elsevier},
     volume = {343},
     number = {12},
     year = {2015},
     doi = {10.1016/j.crme.2015.07.005},
     language = {en},
}

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Anton A. Kutsenko; Alexander L. Shuvalov; Olivier Poncelet; Alexander N. Darinskii. Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance. Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 680-688. doi : 10.1016/j.crme.2015.07.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.07.005/

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