The attenuation of leaky Rayleigh waves due to viscous damping and heat conduction in thin boundary layers is studied by matched asymptotic method. Viscosity of the fluid is considered unimportant except in a thin viscous boundary layer at the interface. By keeping the leading order effect, shown by Re-1/2 = (ων)1/2/ct, where Re is the Reynolds number, ω is the frequency, ν is the kinematic viscosity of the fluid, and ct is the shear velocity of the solid substrate, a new characteristic equation is obtained. One of the numerically obtained solutions gives the leaky Rayleigh wave speed and the attentuation coefficient. It is shown that, together with radiation, viscosity and heat conduction in the boundary layer also contribute to the attenuation of the leaky Rayleigh waves. Furthermore, it is shown that, due to the effect of the viscosity boundary layer, the attenuated leaky Rayleigh wave speed may be smaller than the conventional Rayleigh wave speed at the interface of a solid half space and a vacuum. Moreover, the correction to wave speeds due to viscosity and head conduction is shown to be insignificant for a fluid layer on a solid substrate and can be considered unimportant in most cases. Finally, a new wave mode sustained by the viscous boundary layer alone is discovered in the limit of small fluid - solid density ratio. This mode exists for appropriate frequency-layer thickness combinations. For air the corresponding propagation speed is shown to be higher than the sound speed and the corresponding attenuationis significant. These results may be used to improve our interpretation of experimental results of acoustic signature of materials.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
TAM R 728
1993-6026
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112418
Copyright and License Information
Copyright 1993 Board of Trustees of the University of Illinois
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.
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