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Research Papers

Interfacial Waves With Surface Elasticity

[+] Author and Article Information
Lixin Hu

Department of Mechanical
Aerospace Engineering,
Rutgers University,
Piscataway, NJ 08817
e-mail: lixin.phd@rutgers.edu

Liping Liu

Department of Mechanical Aerospace
Engineering and Department of Mathematics,
Rutgers University,
Piscataway, NJ 08817
e-mail: liu.liping@rutgers.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 6, 2014; final manuscript received April 24, 2014; accepted manuscript posted May 2, 2014; published online May 15, 2014. Assoc. Editor: John Lambros.

J. Appl. Mech 81(8), 081007 (May 15, 2014) (6 pages) Paper No: JAM-14-1096; doi: 10.1115/1.4027579 History: Received March 06, 2014; Revised April 24, 2014; Accepted May 02, 2014

In this paper, we study the existence and uniqueness of interfacial waves in account of surface elasticity at the interface. A sufficient condition for the existence and uniqueness of a subsonic interfacial wave between two elastic half spaces is obtained for general anisotropic materials. Further, we explicitly calculate the dispersion relations of interfacial waves for interfaces between two solids and solid and fluid, and parametrically study the effects of surface elasticity on the dispersion relations. We observe that the dispersion relations of interfacial waves are nonlinear at the presence of surface elasticity and depend on surface elastic properties. This nonlinear feature can be used for probing the bulk and surface properties by acoustic measurements and designing waves’ guides or filters.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Elasticity , Waves
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Figures

Grahic Jump Location
Fig. 1

An elastic interface between two half spaces

Grahic Jump Location
Fig. 2

Dependence of interfacial wave speed on surface elastic modulus Qs(J/m2). v is normalized by the corresponding wave speed v0 for Qs = 0 (ρ1 = 500 kg/m3, ρ2 = 10,000 kg/m3, v1t = v2t = 1000 m/s, and v1l = v2l = 1450 m/s).

Grahic Jump Location
Fig. 3

Dependence of interfacial wave speed on densities ρ1 and ρ2(kg/m3). v is normalized by limiting wave speed v∧ (Qs = 10,000 J/m2, v1t = v2t = 1000 m/s, and v1l = v2l= 1450 m/s).

Grahic Jump Location
Fig. 4

Dependence of interfacial wave speed on bulk wave speeds for given limiting speed v∧ = 2000 m/s. v is normalized by v∧ (Qs = 10,000 J/m2, ρ1 = 500 kg/m3, ρ2 = 10,000 kg/m3, v1t = v2t = 1000 m/s, and v1l = v2l).

Grahic Jump Location
Fig. 5

Dispersion relation of interfacial wave at the interface of aluminum (ρ1 = 2700 kg/m3, v1t = 3040 m/s, and v1l = 6420 m/s) and water (ρ2 = 1000 kg/m3 and vwater = 1484 m/s). Here, surface elastic parameter is Qs = 100,000 J/m2 and interfacial wave speed v is normalized by speed of sound in water vwater.

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