Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Generalized thermoelastic longitudinal waves in unbounded medium

  • 35 Accesses

Summary

In this paper the generalized thermoelastic longitudinal waves and the temperature field set up due to coupling of the displacement and the temperature fields, with heat wave travelling with certain finite velocity, in an unbounded medium are studied. The thermoelastic displacement potential and the temperature field at any point are obtained in terms of the surface integrals involving the potential, the temperature and their normal derivatives.

This is a preview of subscription content, log in to check access.

Abbreviations

x i :

the cartesian coordinate system,i=1,2,3

n :

(u i) the displacement vector

∇:

(δ/δx i) the del operator

δt :

δ/δt the derivative with respect to time

T o :

the temperature corresponding to the natural stat of zero stress and strain

T :

Absolute temperature

c e :

the specific heat

λ, μ:

Lamé's constants

ϱ0 :

the density

α:

coefficient of linear thermal expansion

K :

thermal conductivity coefficient

kk :

u

τ0 :

the relaxation time

References

  1. [1]

    W. Nowacki,Some dynamic problems in thermoelasticity, Arch. Mech. Stos.,11 (1959), 259–283.

  2. [2]

    W. Nowacki,Certain dynamic problems in thermoelasticity, Bull. Acad. Polon. Sci. Ser. Sci. Tech.13 (1956), 657–666.

  3. [3]

    W. Nowacki,Quelques théorèmes de la thermoélasticité, Rev. Roumaine Sci-Tech. Ser. Mech. Appl.11 (1966), 1173–1183.

  4. [4]

    W. Nowacki,Thermoelastic waves in an unbounded medium, Polish Academy of Sciences Warszawa.

  5. [5]

    R. B. Hetnarski,Solution of the coupled problem of thermoelasticity in the form of series of functions. Arch. Mech. Stos.16 (1964), 913–941.

  6. [6]

    H. W. Lord andY. Shulman,A generalized dynamical theory of thermoelasticity, J. Mech. Phy. Solids15 (1967), 299–309.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Singh, H., Singh, A. Generalized thermoelastic longitudinal waves in unbounded medium. PAGEOPH 101, 28–37 (1972). https://doi.org/10.1007/BF00876771

Download citation

Keywords

  • Longitudinal Wave
  • Temperature Field
  • Heat Wave
  • Normal Derivative
  • Surface Integral