Wavefields and band-gaps in layered piezoelectric phononic crystals
UDC
539.3Abstract
The paper describes a mathematical model of plane wave propagation in elastic and piezoelectric layered phononic crystals with a finite number of unit-cells. Wave motion is excited by an incident plane P- or SV- wave coming from an outer elastic half-space. The wavefield is obtained by using the transfer matrix (T-matrix) method. The methods to construct a T-matrix of a piezoelectric layer and T-matrix of the periodic structure consisted of given number of unit-cells are developed. The transmitted wave field is expressed in terms of expansion in eigenvalues of the T-matrix unit-cell. A classification of band-gaps and pass-bands in layered phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of T-matrix for a unit-cell and the asymptotics for the transmission coefficient, when the number of the unit cells tends to infinity. Two kinds of band-gaps, where the transmission coefficient decays exponentially with the number of unit-cells, are specified. The so-called low transmission pass-bands (LTPB) are introduced in order to identify frequency ranges where the wave transmission is very low, but it does not tend to zero exponentially. Very week conversion effects of modes are observed in the LTPB. The types of band-gaps and their transformation with a change of the incident angles are discussed with numerical examples. The influence of piezoelectric and dielectric constants on width and location of band-gaps is studied.
Keywords:
piezoelectric phononic crystal, T-matrix method, band-gap, low transmission pass-bandAcknowledgement
References
- Golenischev-Kutuzov A.V., Golenischev-Kutuzov V.A., Kalimullin R.I. Fotonnyie i fononnyie kristallyi. Formirovanie i primenenie v opto- i akustoelektronike [Photonic and phononic crystals. Their engineering and application in opto- and acoustoelectronics], Moscow, Fiz.-Mat. lit. Publ., 2010. 160 p. (In Russian)
- Lucklum R., Li J., Zubtsov M. 1D and 2D Phononic Crystal Sensors. Procedia Engineering, 2010, vol. 5. P. 436-439.
- Deymier P.A. Acoustic metamaterials and phononic crystals. Springer, 2013, 387 p.
- Khelif A., Adibi A. Phononic Crystals Fundamentals and Applications. Springer-Verlag, New York, 2016. 245 p.
- Yankin S.S., Talbi A., Gerbedoen ZH.-K., Preobrazhenskij V.L., Perno F., Matar O. Bu Rasprostranenie poverhnostnoj akusticheskoj volny v dvumernom fononnom kristalle na p'ezoehlektricheskoj podlozhke [Surface acoustic wave propagation in two-dimensional phononic crystal on a piezoelectric substrate]. Izvestiya Saratovskogo universiteta. Novaya Seriya. Seriya Fizika [News of Saratov University. New series. Series Physics], 2014, vol. 14, no. 2, pp. 5-12. (In Russian)
- Vorovich I.I., Babeshko V.A., Pryahina O.D. Dinamika massivnyih tel i rezonansnyie yavleniya v deformiruemyih sredah [The dynamics of massive objects and resonance phenomena in deformable media]. Moscow: Nauchnyiy mir Publ., 1999, 246 p. (In Russian)
- Glushkov E., Glushkova N., and Zhang C. Surface and pseudo-surface acoustic waves piezoelectically excited in diamond-based structures. J. Appl. Phys., 2012, no. 112, pp. 064911.
- Laude V., Wilm M., Benchabane S., Khelif A. Full band gap for surface acoustic waves in a piezoelectric phononic crystal. Physical Review E., 2005, vol. 71, no. 3, pp. 036607.
- Ponge M.-F., Dubus B., Granger Ch., Vasseur J., Thi M.Ph., Hladky-Hennion A.-Ch. Optimization of a tunable piezoelectric resonator using phononic crystals with periodic electrical boundary conditions. Physics Procedia, 2015, vol. 70, pp. 258-261.
- Darinskii A., Shuvalov A., Poncelet O., Kutsenko A. Bulk longitudinal wave reflection/transmission in periodic piezoelectric structures with metallized interfaces. Ultrasonics, 2015, vol. 63, pp. 118-125.
- Piliposyan D.G., Ghazaryan K.B., Piliposian G.T. Magneto-electro-elastic polariton coupling in a periodic structure. Journal of Physics D: Applied Physics, 2015, vol. 48, no. 17, pp. 175501.
- Golub M.V., Fomenko S.I., Bui T.Q., Zhang Ch., Wang Y.-S. Transmission and band gaps of elastic SH waves in functionally graded periodic laminates. Int. J. of Solids and Structures, 2012, vol. 49, no. 2, pp. 344-354.
- Fomenko S.I. Volnovyie polya i zapreschennyie zonyi v kvaziperiodicheskih sloistyih kompozitah [Wave fields and restricted areas in the quasi-layered composites]. Ekologicheskiy vestnik nauchnyih tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva, 2013, No. 4, Vol. 1, pp. 120-126. (In Russian)
- Fomenko S.I., Golub M.V., Bui T.Q., Zhang Ch., Wang Y.-S. In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals. Int. J. of Solids and Structures, 2014, vol. {51}, no. 13), pp. 2491-2503.
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