Time-domain evolution equation for dispersive nonlinear Rayleigh waves

Won Suk Ohm; Mark F. Hamilton

doi:10.1063/1.2210335

Time-domain evolution equation for dispersive nonlinear Rayleigh waves

Won Suk Ohm, Mark F. Hamilton

Department of Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.

Original language	English
Title of host publication	INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA 17
Subtitle of host publication	17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum
Pages	139-142
Number of pages	4
DOIs	https://doi.org/10.1063/1.2210335
Publication status	Published - 2006
Event	INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum - State College, PA, United States Duration: 2005 Jul 18 → 2005 Jul 22

Publication series

Name	AIP Conference Proceedings
Volume	838
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Other

Other	INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum
Country	United States
City	State College, PA
Period	05/7/18 → 05/7/22

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1063/1.2210335

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title = "Time-domain evolution equation for dispersive nonlinear Rayleigh waves",

abstract = "Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.",

author = "Ohm, {Won Suk} and Hamilton, {Mark F.}",

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language = "English",

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series = "AIP Conference Proceedings",

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booktitle = "INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA 17",

note = "INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum ; Conference date: 18-07-2005 Through 22-07-2005",

}

Ohm, WS & Hamilton, MF 2006, Time-domain evolution equation for dispersive nonlinear Rayleigh waves. in INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA 17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum. AIP Conference Proceedings, vol. 838, pp. 139-142, INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, State College, PA, United States, 05/7/18. https://doi.org/10.1063/1.2210335

Time-domain evolution equation for dispersive nonlinear Rayleigh waves. / Ohm, Won Suk; Hamilton, Mark F.

INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA 17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum. 2006. p. 139-142 (AIP Conference Proceedings; Vol. 838).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.

AB - Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.

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Time-domain evolution equation for dispersive nonlinear Rayleigh waves

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