Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides

Günter Leugering, Sergei A. Nazarov, Jari Taskinen

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.

Original languageEnglish
Pages (from-to)69-111
Number of pages43
JournalAsymptotic Analysis
Volume111
Issue number2
DOIs
StatePublished - 1 Jan 2019

Keywords

  • Asymptotic decomposition
  • Detached asymptotics
  • Limited absorption principle
  • Mandelstam principle
  • Piezo-elasticity
  • Piezo-electricity
  • Sommerfeld principle
  • Umov-Poynting vector
  • Waveguide

Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides",
abstract = "We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.",
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Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides. / Leugering, Günter; Nazarov, Sergei A.; Taskinen, Jari.

In: Asymptotic Analysis, Vol. 111, No. 2, 01.01.2019, p. 69-111.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides

AU - Leugering, Günter

AU - Nazarov, Sergei A.

AU - Taskinen, Jari

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N2 - We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.

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KW - Piezo-electricity

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