Journal of Elasticity

, Volume 124, Issue 2, pp 193–223 | Cite as

Trapped Modes in Piezoelectric and Elastic Waveguides

  • Sergei A. Nazarov
  • Keijo M. RuotsalainenEmail author
  • Minna Silvola


We derive a sufficient condition for the existence of trapped modes in a cylindrical piezoelectric waveguide \(\varOmega\) with a compact void \(\varTheta\). An infinite part \(\varGamma_{D}\) of the exterior boundary \(\partial\varOmega\) is clamped along an electric conductor and the remaining part \(\varGamma_{N}=(\partial\varOmega\setminus \varGamma_{D})\cup\partial\varTheta\) is traction-free and is in contact with an insulator, e.g., a vacuum. The condition permits the limit passage either to an elastic or a compound waveguide but it crucially differs from the pure elastic case due to the involved electric enthalpy instead of the energy functional. Examples of concrete waveguides and voids supporting trapped modes are given, and open questions are formulated. In particular, in contrast to a pure elastic waveguide where “almost” any crack traps a wave, no example of a crack trapping a wave in a piezoelectric waveguide is known yet.


Trapped mode Piezoelectricity Waveguide 

Mathematics Subject Classification

35P15 35Q74 74F15 74F20 



The first author is supported by the Russian Foundation of Basic Research grant 15-01-02175.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Peter the Great Saint-Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.Institute of Problems Mechanical Engineering RASSt. PetersburgRussia
  4. 4.Applied and Computational Mathematics Research GroupUniversity of OuluOuluFinland

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