JAMP  Vol.2 No.10 , September 2014
A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media
Abstract: The work deals with a mathematical model for real-time acoustic monitoring of material parameters of media in multi-state viscoelastic engineering systems continuously operating in irregular external environments (e.g., wind turbines in cold climate areas, aircrafts, etc.). This monitoring is a high-reliability time-critical task. The work consistently derives a scalar wave PDE of the Stokes type for the non-equilibrium part (NEP) of the average normal stress in a medium. The explicit expression for the NEP of the corresponding pressure and the solution-adequateness condition are also obtained. The derived Stokes-type wave equation includes the stress relaxation time and is applicable to gases, liquids, and solids.
Cite this paper: Mamontov, E. and Berbyuk, V. (2014) A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media. Journal of Applied Mathematics and Physics, 2, 960-970. doi: 10.4236/jamp.2014.210109.

[1]   Rose, J.L. (1999) Ultrasonic Waves in Solid Media. Cambridge University Press, Cambridge.

[2]   Datta, S.K. and Shah, A.H. (2009) Elastic Waves in Composite Media and Structures: With Applications to Ultrasonic Nondestructive Evaluation. CRC Press, Boca Raton.

[3]   Grad, H. (1958) Principles of the Kinetic theory of Gases. In: Flügge, S. Ed., Handbuch der Physik, Band XII, Springer-Verlag, Berlin, 205-294.

[4]   Balescu, R. (1997) Statistical Dynamics: Matter out of Equilibrium. Imperial College Press, London.

[5]   Pollard, H.F. (1977) Sound Waves in Solids. Pion, London.

[6]   Landau, L.D. and Lifshitz, E.M. (1986) Theory of Elasticity. Pergamon Press, Oxford.

[7]   Stokes, G.G. (1845) On the Theories of the Internal Friction of Fluids in Motion and of the Equilibrium and Motion of Elastic Solids. Trans. Cambridge Philos. Soc., 8, 287-319.

[8]   Merkel, H. (2006) Apparatus and a Method for Determining the Spatial Distribution of Physical Parameters in an Object. US Patent Application 11/375,133, 20.

[9]   Landau, L.D. and Lifshitz, E.M. (1987) Fluid Mechanics. Pergamon Press, Oxford.

[10]   Koshlyakov, N.S., Smirnov, M.M. and Gliner, E.B. (1964) Differential Equations of Mathematical Physics. North-Holland Publishing, Amsterdam.

[11]   Longman, I.M. (1980) Wave Propagation in a Viscoelastic Solid. Journal of Computational Physics, 37, 171-182.

[12]   Ricker, N.H. (1977) Transient Waves in Visco-Elastic Media. Elsevier, Amsterdam.

[13]   Sedov, L.I. (1971) A Course in Continuum Mechanics. Vol. 1, Wolters-Noordhoff, Groningen.

[14]   Trigg, G.L. (1991) Encyclopedia of Applied Physics, Vol. 1, VCB, New York.

[15]   Dukhin, A., et al. (2014) Volume Viscosity, Wikipedia. Wikimedia Foundation, Inc.

[16]   Goldstein, H. (1980) Classical Mechanics. Addison-Wesley, Reading.