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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.

has been cited by the following article:

• TITLE: A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media

  AUTHORS: Eugen Mamontov, Viktor Berbyuk

  KEYWORDS: Acoustic Monitoring, Gas, Liquid, or Solid, Acoustic Equation, Visoelastic Media, Stress Relaxation Time, Average Normal Stress, the Stokes-Type Wave Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.10, September 30, 2014

  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.