×

zbMATH — the first resource for mathematics

On the coupling of guided waves propagation in piezoelectric crystals subject to initial fields. (English) Zbl 1257.74092
Summary: This paper deals with the study of the coupling conditions for propagation of planar guided waves in a piezoelectric semi-infinite plane (called sagittal plane) subject to initial electro-mechanical fields. The piezoelectric material behaves linearly and without attenuation and the waveguide propagates in a normal mode. We suppose that the material is subject to initial electro-mechanical fields. If the sagittal plane is normal to a direct, resp. inverse dyad axis, we derive that the fundamental equations’ system decomposes for particular choices of the initial electric field. In this way we obtain mechanical and piezoelectric waves generalizing the classical guided waves from the case without initial fields. Furthermore, we obtain a similar decomposition of mechanical and electrical boundary conditions, which enable us to characterize the obtained guided waves.

MSC:
74J99 Waves in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74E15 Crystalline structure
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baumhauer, J.C., Journal of the Acoustic Society of America 54 pp 1017– (1973) · Zbl 0274.73058
[2] Chai, J.F., Journal of the Acoustic Society of America 100 pp 2112– (1996)
[3] Hu, Y., Zeitschrift für Angewandte Mathematik und Physik 55 pp 678– (2004)
[4] Tiersten, H.F., International Journal of Engineering Science 33 pp 2239– (1995) · Zbl 0899.73451
[5] Yang, J., Mechanics Research Communications 28 pp 679– (2001) · Zbl 1048.74020
[6] Yang, J., Applied Mechanics Review 57 pp 173– (2004)
[7] Eringen, A.C., Electrodynamics of Continua, Vol. I (1990) · Zbl 0568.73106
[8] Baesu, E., Zeitschrift für Angewandte Mathematik und Physik 54 pp 160– (2003) · Zbl 1029.74017
[9] Simionescu, O., Mathematics and Mechanics of Solids 6 pp 437– (2001) · Zbl 1018.74019
[10] Simionescu-Panait, O., International Journal of Applied Electromagnetics and Mechanics 12 pp 241– (2000)
[11] Simionescu-Panait, O., Mathematics and Mechanics of Solids 6 pp 661– (2001) · Zbl 1019.74019
[12] Simionescu-Panait, O., Mechanics Research Communications 28 pp 685– (2001) · Zbl 1071.74030
[13] Simionescu-Panait, O., Zeitschrift für Angewandte Mathematik und Physik 53 pp 1038– (2002) · Zbl 1031.74032
[14] Simionescu-Panait, O., Proceedings of International Conference on New Trends in Continuum Mechanics · Zbl 1090.74040
[15] Simionescu-Panait, O., Mathematical Reports 8 (58) pp 239– (2006)
[16] Simionescu-Panait, O., International Journal of Applied Electromagnetics and Mechanics 22 pp 111– (2005) · Zbl 1090.74040
[17] Simionescu-Panait, O., Proc. of Fourth Workshop on Mathematical Modelling of Environmental and Life Sciences Problems · Zbl 1150.74425
[18] Simionescu-Panait, O., Revue Roumaine de Mathématiques Pures et Appliquées 51 pp 379– (2006)
[19] Simionescu-Panait, O., Mathematics and Mechanics of Solids 12 pp 107– (2007) · Zbl 1149.74033
[20] Fedorov, F.I., Theory of Elastic Waves in Crystals (1968)
[21] Royer, D., Elastic Waves in Solids, I-Free and Guided Propagation (2000) · Zbl 0960.74002
[22] Sirotin, I.I., Crystal Physics (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.