Near Incompressibility at Uniform Temperature or Entropy in Isotropic Thermoelasticity

Abstract

This article is concerned with longitudinal wave propagation in an isotropic thermoelastic material that is nearly incompressible at either uniform temperature or uniform entropy. A dimensionless effective bulk modulus X is defined such that X-+ oo corresponds to incompressibility at uniform temperature. For 0 < X < 1, both longitudinal waves are stable, but for X > 1, one is stable and the other unstable. If X = 1, there is only one propagating mode, and this is stable. Another dimensionless effective bulk modulus X is defined such that X -+ oo corresponds to incompressibility at uniform entropy. For 0 < X < oo, both longitudinal waves are stable. Making the identification X = x/(1-X), among others, enables the equivalence of the two types of near constraint to be demonstrated. In particular, X -* oo corresponds to-+ 1-, so that incompressibility at uniform entropy corresponds to near incompressibility at constant temperature. Many graphical results are presented to illustrate various points of theory.