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

Leugering G, Nazarov SA, Taskinen J (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Asymptotic Analysis IOS Press

Book Volume: 111

Pages Range: 69-111

Journal Issue: 2

DOI: 10.3233/ASY-181487

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.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Involved external institutions

Saint Petersburg State University (SPbU) / Санкт-Петербургский государственный университет (СПбГУ) RU Russian Federation (RU) Helsingin yliopisto / University of Helsinki FI Finland (FI)

How to cite

APA:

Leugering, G., Nazarov, S.A., & Taskinen, J. (2019). Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides. Asymptotic Analysis, 111(2), 69-111. https://doi.org/10.3233/ASY-181487

MLA:

Leugering, Günter, Sergei A. Nazarov, and Jari Taskinen. "Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides." Asymptotic Analysis 111.2 (2019): 69-111.

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