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.