Generalized Rayleigh waves in thermoelastic solids under viscous fluid loading

• Autorzy: Sharma J. N. , Sharma R. , Sharma Y. D.
• Języki publikacji: EN

Abstrakty

EN

The paper is aimed to study the propagation of Rayleigh surface waves in a homogeneous isotropic, thermally condueting, and elastic solid halfspace underlying a viscous liquid semi space in the context of generalized theories of thermoelasticity. The investigation is based on modelling the viscous liquid as a hypothetical solid in addition to conduction-convection condition of heat transfer at the interface. After developing the mathematical model, boundary conditions and formal solutions, the secular equations for a thermoelastic solid in closed form and isolated mathematical conditions for generalized Rayleigh waves (Stoneley waves), in complete forms are derived. The amplitude ratios of solid and liquid displacements and temperature change on the surface (interface) are obtained analytically. The surface particle motion has also been discussed and found to be elliptical. The semi-major and semi-minor axes, eccentricity and inclination of major axes with the wave normal are computed analytically and analyzed numerically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) underlying water, in the case of both light and heavy semi spaces. The dispersion curves, attenuation coefficient profiles and amplitude ratios of surface displacements, temperature change in the solid half space for generalized Rayleigh waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The present analysis is useful in electronics and navigation applications.

Słowa kluczowe

EN

thermal relaxation; Rayleigh waves; attenuation; particle paths; viscous fluid

PL

fala Rayleigha; tłumienie sygnału; płyny lepkie

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2008
• Tom: Vol. 13, no 1
• Strony: 217--238
• Opis fizyczny: Bibliogr. 30 poz., wykr.

Twórcy

autor

Sharma J. N.

autor

Sharma R.

autor

Sharma Y. D.

• Department of Mathematics National Institute of Technology Hamlrpur - 177005 INDIA,

Bibliografia

• Andle J.C. and Vetelino J.F.(1994): Acoustic Wave Biosensors. Sensors and Actuators. - A, vol.44, pp.167-176.
• Ackerman C.C., Bentman B., Fairbank H.A. and Krumhansal R.A. (1966): Second sound in helium. - Physical Review Letters, vol.16, pp.789-791.
• Ackerman C.C. and Overtone W.C. (1969): Second sound in helium-3. - Physical Review Letters, vol.22, pp.764-766.
• Achenbach J.D. (1973): Wave Propagation in Elastic Solids. - North-Holland, America: Elsevier.
• Achenbach J.D. (2005): The thermoelasticity of laser- based ultrasonics. - Journal of Thermal Stresses, vol.28, pp.713-72.
• Chandrasekharaiah D.S. (1986): Thermoelasticity with second sound -a review. - Applied Mechanics Reviews, vol.39, pp.355-376.
• Chadwick P. and Windle D.W. (1964): Propagation of Rayleigh Waves along isothermal and insulated boundaries. - Proceedings of the Royal Society of America, vol.280, pp.47-71.
• Chadwick P. and Atkins R.J. (1981): Surface waves in heat conducting elastic body-Correction and extension of paper of Chadwick and Windle. - Journal of Thermal Stresses, vol.4, pp.509-521.
• Ewing M., Jardetzky W.S. and Press F. (1957): Elastic Waves in Layered Media. - New York: McGraw-Hill, pp.272-280.
• Green A.E. and Lindsay K.A. (1972): Thermoelasticity. - Journal of Elasticity, vol.2, pp.1-7.
• Guyer R.A. and Krumhansal J.A. (1966): Thermal conductivity, second sound and phonon hydrodynamic phenomenon in nonmetallic crystals. - Physical Review, vol.148, pp.778-781.
• Graff K.F. (1991): Wave Motion in Elastic Solids. - New York: Dover.
• Kim J.O. and Achenbach J.D. (1992): Elastic constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy. - Journal of Applied Physics, vol.72, No.5, pp.1805-1811.
• Kovacs G., Vellekoop M.J., Haueis R., Lubking G.W. and Venema A. (1994): A Love wave sensor for (bio) chemical sensing in liquids. - Sensors and Actuators, A, vol.43, pp.38-43.
• Kurtze G. and Bolt R.H. (1959): On the interaction between plate bending wave and radiation load. - Acoustica, vol.9, pp.238-242.
• Lord H.W. and Shulman Y. (1967): A generalized dynamical theory of thermoelasticity. - Journal of Mechanics and Physics of Solids, vol.15, pp.299-309.
• Lockett F.J. (1958): Effect of thermal properties of a solid on the velocity of Rayleigh waves. - Journal of Mechanics and Physics of Solids, vol.7, pp.71-75.
• Nayfeh A.H. and Nagy P.B. (1997): Excess attenuation of leaky Lamb waves due to viscous fluid loading. - Journal of the Acoustical Society of America, vol.101, pp.2649-2658.
• Nayfeh A.H. and Nasser S.N. (1971): Thermoelastic waves in solids with thermal relaxation. - Acta Mechanica, vol.12, pp.53-69.
• Qi Q. (1994): Attenuated Leaky Lamb Waves. - Journal of Acoustical Society of America, vol.95, pp.3222-3231.
• Cooper R.D., Gillespie W.H.B., A. B. and Pike R.B. (1982): The attenuation of Lamb waves in the presence of fluid. - Ultrasonics, vol.20, pp.257-262.
• Stroh A.N. (1962): Steady state problems in anisotropic elasticity. - Journal of Mathematical Physics, vol.41, pp.77-103.
• Schoch V.A. (1952): Der Schalldurchgang Durch Platten (Sound Transmission in Plates). - Acoustica, vol.2, pp.1-17.
• Scholte J.G. (1949): On true and pseudo Rayleigh waves. - Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen Series, vol.52, pp.652-653.
• Sharma J.N. and Pathania V. (2005): Propagation of leaky surface waves in thermoelastic solids due to inviscid fluid loadings. - Journal of Thermal Stresses, vol.28, pp.485-519.
• Sharma J.N. and Pathania V. (2003): Generalized thermoelastic Lamb waves in a plate bordered with Layers of inviscid liquid. - Journal of Sound and Vibration, vol.268, pp.897-916.
• Strunin D.V. (2001): On characteristic times in generalized thermoelasticity. - Journal of Applied Math., vol.68, pp.816-817.
• Sharma J.N., Singh D. and Kumar R. (2000): Generalized thermoelastic waves in a homogeneous isotropic plates. - Journal of the Acoustical Society of America, vol.108, pp.848-851.
• Wu J.R. and Zhu Z.M. (1992): The propagation of Lamb waves in a plate bordered with layers of a liquid. - Journal of the Acoustical Society of America, vol.91, pp.861-867.
• Zhu Z. and Wu J. (1995): The propagation of Lamb waves in a plate bordered with viscous liquid. - Journal of the Acoustical Society of America, vol.98, pp.1057-1067.