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International Journal of Thermophysics

, Volume 30, Issue 6, pp 2078–2097 | Cite as

Effect of Rotation in a Generalized Thermoelastic Medium with Hydrostatic Initial Stress Subjected to Ramp-Type Heating and Loading

  • Praveen Ailawalia
  • Naib Singh Narah
Article

Abstract

The present problem is concerned with the study of deformation of a rotating generalized thermoelastic medium with a hydrostatic initial stress. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The components of displacement, force stress, and temperature distribution are obtained in the Laplace and Fourier domains by applying integral transforms. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results are also presented graphically to show the effect of rotation and hydrostatic initial stress.

Keywords

Generalized thermoelasticity Hydrostatic initial stress Laplace and Fourier transforms Ramping parameter Rotation Temperature distribution 

List of symbols

λ, μ

Lame’s constants

ρ

Density

\({\vec{u}}\)

Displacement vector

tij

Stress tensor

\({\tau _0, \vartheta _0}\)

Thermal relaxation times

v = (3λ + 2μ) αt

Linear thermal expansion

\({e={\rm{div}}\vec {u}}\)

Dilatation

\({K^{{\bullet}}}\)

Coefficient of thermal conductivity

CE

Specific heat

t0

Ramping parameter

p

Initial pressure

η

Initial stress parameter

E

Young’s modulus

σ

Poisson ratio

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Applied Sciences, M.M. Engineering CollegeMaharishi Markandeshwar UniversityAmbalaIndia
  2. 2.Department of MathematicsD.A.V. CollegeAmbala CityIndia

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