Skip to main content
SpringerLink
Log in

Electroelastic Wave

  • Chapter
  • First Online:
Theory of Electroelasticity

Abstract

In this chapter the electroelastic wave in piezoelectric and pyroelectric materials are discussed. In the electrically quasi-static approximation in an infinite space, there are three independent elastic waves for the piezoelectric material, and there is no independent electric wave. In the pyroelectric material a temperature wave has happened. In the reflection and transmission of waves, the inhomogeneous wave theory is effective; a quasi-surface wave is revealed in the electrically quasi-static approximation. In some particular cases the coupling between elastic equation and Maxwell electrodynamics equation needs to be studied together, and in these cases there are three elastic waves and two electric waves in the piezoelectric material. Surface acoustic waves (SAW) are extensively used in engineering. In order to improve performance of SAW devices, SAW devices may work in a biasing state. In this chapter a small perturbation superposed on finite generalized displacements is discussed in detail, and some surface waves under the biasing state are studied. The inertial entropy theory is used to derive the governing equation of the temperature wave with finite propagation velocity. The general dynamic analyses of interface cracks are given shortly, and some wave scattering problems from a crack tip are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Achenbach J, Keer L, Mendelsohn D (1980) Elastodynamic analysis of an edge crack. J Appl Mech 47:551–556

    Article  MathSciNet  MATH  Google Scholar 

  • Assour MB, Elmazria O, Rioboo RJ, Sarry PA (2000) Modelling of SAW filter based on \( {{\mathrm{ ZnO}} \left/ {{{{\mathrm{ diamond}} \left/ {\mathrm{ Si}} \right.}}} \right.} \) layered structure including velocity dispersion. Appl Surf Sci 164:200–204

    Article  Google Scholar 

  • Auld BA (1973) Acoustic fields and waves in solids. Wiley, New York

    Google Scholar 

  • Babich VM, Lukyanov VV (1998) Wave propagation along a curved piezoelectric layer. Wave Motion 28:1–11

    Article  MathSciNet  MATH  Google Scholar 

  • Banerjee DK, Bao YH (1974) Thermoelastic waves in anisotropic solids. J Acoust Soc Am 56:1444–1454

    Article  MATH  Google Scholar 

  • Biryukov SV, Gulyaev YV, Kryiov VV, Plessky VP (1995) Surface acoustic waves in inhomogeneous media. Springer, New York

    Book  MATH  Google Scholar 

  • Bleustein JL (1968) A new surface wave in piezoelectric materials. Appl Phys Lett 13:412–413

    Article  Google Scholar 

  • Borcherdt RD (1973) Energy and plane waves in linear viscoelastic media. J Geophys Res 78:2442–2453

    Article  Google Scholar 

  • Buchen PW (1971) Plane waves in linear viscoelastic media. Geophys J R Astron Soc 23:531–542

    Article  MATH  Google Scholar 

  • Cattaneo C (1958) Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanee. Comptes Rendus de l’Académie des Sciences Paris 247:431–433

    MathSciNet  Google Scholar 

  • Chen J, Liu Z-X (2005) On the dynamic behavior of a functionally graded piezoelectric strip with periodic cracks vertical to the boundary. Int J Solids Struct 42:3133–3146

    Article  MATH  Google Scholar 

  • Chen Z-T, Karihaloo BL, Yu S-W (1998) A Griffith moving crack along the interface of two dissimilar piezoelectric materials. Int J Fract 91:197–203

    Article  Google Scholar 

  • Cho Y, Yamanouchi K (1987) Nonlinear, elastic, piezoelectric, electrostrictive and dielectric constants of Lithium niobate. J Appl Phys 61:875–886

    Article  Google Scholar 

  • Danoyan ZN, Pilliposian GT (2007) Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and a dielectric layer. Int J Solids Struct 44:5829–5847

    Article  MATH  Google Scholar 

  • Darinskii AN, Le Clezio E, Feuillard G (2008) The role of electromagnetic waves in the reflection of acoustic waves in piezoelectric crystals. Wave Motion 45:428–444

    Article  MathSciNet  MATH  Google Scholar 

  • Dieulesaint E, Royer D (1980) Elastic waves in solids. Translated by Bastin A, Motz M. Wiley, New York

    Google Scholar 

  • Du J, Xian K, Wang J, Young Y-K (2008) Propagation of Love waves in prestressed piezoelectric layered structures loaded with viscous liquid. Acta Mech Solida Sin 21:542–548

    Google Scholar 

  • Erdogan F (1975) Complex function technique. In: Continuum physics, vol II. Academic, New York

    Google Scholar 

  • Erdogan F, Gupta GD (1972) On the numerical solution of singular integral equations. Q Appl Math 32:525–553

    Google Scholar 

  • Every AG, Neiman VI (1992) Reflection of electroacoustic waves in piezoelectric solids: mode conversion into four bulk waves. J Appl Phys 71:6018–6024

    Article  Google Scholar 

  • Ezzat MA, Otman MI, Ei-Karamany AS (2002) State space approach to generalized thermo-viscoelasticity with two relaxation times. Int J Eng Sci 40:283–302

    Article  Google Scholar 

  • Fischer FA (1955) Fundamentals of electroacoustics. Interscience, New York

    Google Scholar 

  • Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7

    Article  MATH  Google Scholar 

  • Gulyaev YV (1969) Electroacoustic surface waves in solids. Soviet Phys-JETP (A translation of the “J Exp Theor Phys Acad Sci USSR”) 9:37–38

    Google Scholar 

  • Ing Y-S, Wang M-J (2004a) Explicit transient solutions for a mode-III crack subjected to dynamic concentrated loading in a piezoelectric medium. Int J Solids Struct 41:3849–3864

    Article  MATH  Google Scholar 

  • Ing Y-S, Wang M-J (2004b) Transient analysis of a mode-III crack propagating in a piezoelectric medium. Int J Solids Struct 41:6197–6214

    Article  MATH  Google Scholar 

  • Jackson HE, Walker CT (1971) Thermal conductivity, second sound and phonon-phonon interactions in NaF. Phys Rev B 3:1428–1439

    Article  Google Scholar 

  • Jin F, Wang Z-K, Wang T-J (2001) The Bleustein-Gulyaev (B-G) Wave in a piezoelectric layered half-space. Int J Eng Sci 39:1271–1285

    Article  Google Scholar 

  • Joseph DD, Preziosi L (1989) Heat waves. Rev Mod Phys 61:41–73

    Article  MathSciNet  MATH  Google Scholar 

  • Joseph DD, Preziosi L (1990) Addendum to the paper: heat waves. Rev Mod Phys 62:375–391

    Article  MathSciNet  Google Scholar 

  • Joshi SG, Jin Y (1991) Propagation of ultrasonic lamb waves in piezoelectric plates. J Appl Phys 70:4113–4120

    Article  Google Scholar 

  • Kaliski S (1965) Wave equation of thermoelasticity. Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Techniques 13:211–219

    Google Scholar 

  • Khuri-Yakub BT, Kino GS (1974) A monolithic zinc-oxide-silicon convolver. Appl Phys Lett 25:188–193

    Article  Google Scholar 

  • Krebes ES (1983) The viscoelastic reflection/transmission problem: two special cases. Bull Seismol Soc Am 73:1673–1683

    Google Scholar 

  • Kuang Z-B (2002) Nonlinear continuum mechanics. Shanghai Jiaotong University Press, Shanghai (in Chinese)

    Google Scholar 

  • Kuang Z-B (2009) Variational principles for generalized dynamical theory of thermopiezoelectricity. Acta Mech 203:1–11

    Article  MATH  Google Scholar 

  • Kuang Z-B (2011) Some thermodynamic problems in continuum mechanics. In: Piraján JCM (ed) Thermodynamics – kinetics of dynamic systems. Intech Open Access Publisher, Croatia

    Google Scholar 

  • Kuang Z-B, Yuan X-G (2011) Reflection and transmission theories of waves in pyroelectric and piezoelectric materials. J Sound Vib 330:1111–1120

    Article  Google Scholar 

  • Kuang Z-B, Zhou Z-D (2012) Waves in pyroelectric materials. ICTAM, Beijing

    Google Scholar 

  • Kyame JJ (1949) Wave propagation in piezoelectric crystals. J Acoust Soc Am 21:159–167

    Article  Google Scholar 

  • Landau L (1941) The theory of superfluidity of helium II. J Phys 5:71–90

    Google Scholar 

  • Laurent T, Bastien FO, Pommier J, Cachard A, Remiens D, Cattan E (2000) Lamb wave and plate mode in ZnO/Silicon and AIN/Silicon membrane application to sensors able to operate in contact with liquid. Sens Actuators 87:26–37

    Article  Google Scholar 

  • Lavrenchive MA, Shabat VA (1951) Method and theory of complex functions. National Technical and Theoretical Literature Press, Moscow; Лаврентьев МА, Шабат ВА (1951) Метод теории фукций коплекснго переменого. Государственное издадельство. технико – теоретический литературы. Москвa

    Google Scholar 

  • Li S (1996) The electromagneto-acoustic surface wave in a piezoelectric medium: the Bleustein-Gulyaev mode. J Appl Phys 80:5264–5269

    Article  Google Scholar 

  • Li S (2000) Transient wave propagation in a transversely isotropic piezoelectric half space. Z Angew Math Phys 51:236–266

    Article  MathSciNet  MATH  Google Scholar 

  • Li S, Mataga PA (1996) Dynamic crack propagation in piezoelectric materials-part I. electrode solution, J Mech Phys Solids 44:1799–1830

    Google Scholar 

  • Li C, Weng GJ (2002) Yoffe-type moving crack in a functionally graded piezoelectric material. Proc R Soc Lond A 458:381–399

    Article  MathSciNet  MATH  Google Scholar 

  • Li S, To AC, Glaser SD (2005a) On scattering in a piezoelectric medium by a conducting crack. J Appl Mech 72:943–954

    Article  MATH  Google Scholar 

  • Li X-F, Yang JS, Jiang Q (2005b) Spatial dispersion of short surface acoustic waves in piezoelectric ceramics. Acta Mech 180:11–20

    Article  MATH  Google Scholar 

  • Lionetto F, Montagna F, Maffezzoli A (2005) Ultrasonic dynamic mechanical analysis of polymers. Appl Rheol 15:326–335

    Google Scholar 

  • Liu Y, Wang C-h, Ying CF (1989) Electromagnetic acoustic head waves in piezoelectric media. Appl Phys Lett 55:434–436

    Article  Google Scholar 

  • Liu H, Wang Z-K, Wang T-J (2001) Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. Int J Solids Struct 38:37–51

    Article  MATH  Google Scholar 

  • Liu H, Wang T-J, Wang Z-K, Kuang Z-B (2002a) Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates. Int J Solids Struct 39:1777–1790

    Article  MATH  Google Scholar 

  • Liu H, Wang T-J, Wang Z-K, Kuang Z-B (2002b) Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates. Int J Solids Struct 39:2031–2049

    Article  MATH  Google Scholar 

  • Liu H, Kuang Z-B, Cai Z-M (2003a) Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure. Ultrasonics 41:397–405

    Article  Google Scholar 

  • Liu H, Kuang Z-B, Cai Z-M (2003b) Application of transfer matrix method in analyzing the inhomogeneous initial stress problem in prestressed layered piezoelectric media. In: Watanabe K, Ziegler F (eds) IUTAM symposium on dynamics of advanced materials and smart structures. Kluwer Academic Publishers, Dordrecht/Boston/London

    Google Scholar 

  • Liu H, Kuang Z-B, Cai Z-M (2003c) Love wave in non-homogeneous layered structures. Acta Mech Sin 35:485–488

    Google Scholar 

  • Liu H, Kuang Z-B, Cai Z-M (2003d) Propagation of surface acoustic waves in prestressed anisotropic layered piezoelectric structures. Acta Mech Solida Sin 16:16–23

    Google Scholar 

  • Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309

    Article  MATH  Google Scholar 

  • Lu C-K (1984) A class of quadrature formulas of Chebyshev type for singular integrals. J Math Anal Appl 100:416–435

    Article  MathSciNet  MATH  Google Scholar 

  • Ma XJ, Liu FS, Zhang MJ, Sun YY (2011) Viscosity of aluminum under shock-loading conditions. Chin Phys B 20:068301–068304

    Article  Google Scholar 

  • Meikumyan A (2007) On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode. Int J Solids Struct 44:3811–3827

    Article  Google Scholar 

  • Mindlin RD (1968) Polarization gradient in elastic dielectrics. Int J Solids Struct 4:637–642

    Article  MATH  Google Scholar 

  • Mineev VN, Mineev AV (1997) Viscosity of metals under shock-loading conditions. J De Phys IV 7(C3):583–585

    Google Scholar 

  • Nayfen A (1995) Wave propagation in layered anisotropic media. Elsevier, Amsterdam

    Google Scholar 

  • Noble B (1958) Methods based on the wiener-Hopf technique. Pergamon Press, New York

    MATH  Google Scholar 

  • Ogden RW (1984) Nonlinear elastic deformations. Ellis Horwood/Halsted Press, Chichester/New York

    MATH  Google Scholar 

  • Pang Y, Wang Y-S, Liu J-X, Fang D-N (2008) Reflection of plane waves at the interface between piezoelectric piezomagnetic media. Int J Eng Sci 46:1098–1110

    Article  MathSciNet  MATH  Google Scholar 

  • Sharma JN, Pal M (2004) Propagation of Lamb waves in a transversely isotropic piezothermoelastic plate. J Sound Vib 270:587–610

    Article  Google Scholar 

  • Sharma JN, Walia V, Gupta SK (2008) Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space. Int J Eng Sci 46:131–146

    Article  MathSciNet  MATH  Google Scholar 

  • Shen S-P, Nishioka T, Kuang Z-B (1999) Impact interfacial fracture for piezoelectric ceramic. Mech Res Commun 26:347–352

    Article  MATH  Google Scholar 

  • Shen S-P, Kuang Z-B, Nishioka T (2000) Dynamics mode-III interfacial crack in nonlinear piezoelectric materials. Int J Appl Electromagn Mech 11:211–222

    Google Scholar 

  • Sinha AK, Tanski WJ, Lukaszek T, Ballato A (1985) Influence of biasing stress on the propagation of surface waves. J Appl Phys 57:767–776

    Article  Google Scholar 

  • Stewart JT, Yong YK (1994) Exact analysis of the propagation of acoustic waves in multilayered anisotropic piezoelectric plate. IEEE Trans Ultrason Ferroelectr Freq Control 41:375–390

    Article  Google Scholar 

  • Su J, Liu H, Kuang Z-B (2005) Love wave in ZnO/SiO2/Si structure with initial stresses. J Sound Vib 286:981–999

    Article  Google Scholar 

  • Thomson WT (1950) Transmission of elastic waves through a stratified solid medium. J Appl Phys 21:89–93

    Article  MathSciNet  MATH  Google Scholar 

  • Tiersten HF (1978) Perturbation theory for linear electroelastic equations for small fields superposed on a bias. J Acoust Soc Am 64:832–837

    Article  MATH  Google Scholar 

  • Vernotte P (1958) Les paradoxes de la théorie continue de l’equation de la chaleeur. Comptes Rendus de l’Académie des Sciences Paris 246:3154–3155

    MathSciNet  Google Scholar 

  • Wang X-Y, Yu S-W (2001) Transient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-I problem. Mech Mater 33:11–20

    Article  Google Scholar 

  • Yuan X-G, Kuang Z-B (2008) Waves in pyroelectrics. J Therm Stress 31:1190–1211

    Article  Google Scholar 

  • Yuan X-G, Kuang Z-B (2010) The inhomogeneous waves in pyroelectrics. J Therm Stress 33:172–186

    Article  Google Scholar 

  • Zhou Z-D, Yang F-P, Kuang Z-B (2012) Reflection and transmission of plane waves at the interface of pyroelectric bi-materials. J Sound Vib 331:3558–3566

    Article  Google Scholar 

  • Zhu J-J, Kuang Z-B (1995) On interface crack propagation with variable velocity for longitudinal shear problems. Int J Fract 72:121–144

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China, People’s Republic

    Zhen-Bang Kuang

Authors
  1. Zhen-Bang Kuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kuang, ZB. (2014). Electroelastic Wave. In: Theory of Electroelasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36291-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36291-0_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36290-3

  • Online ISBN: 978-3-642-36291-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation