scholarly journals Thermoelastic Displacements and Stresses Due to a Heat Source Moving Over the Surface of a Half Plane

1984 ◽  
Vol 51 (3) ◽  
pp. 636-640 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Heat Source ◽  
Point Source ◽  
Half Plane ◽  
Bessel Functions ◽  
Surface Displacement ◽  
Constant Speed ◽  
Line Heat Source ◽  
Asymptotic Expressions ◽  
Instantaneous Point

A solution is given for the surface displacement and stresses due to a line heat source that moves at constant speed over the surface of an elastic half plane. The solution is obtained by integration of previous results for the instantaneous point source. The final results are expressed in terms of Bessel functions for which numerically efficient series and asymptotic expressions are given.

Steady-State Motion of a Line Mechanical/Heat Source Over a Half-Space: A Thermoelastodynamic Solution

1997 ◽  
Vol 64 (3) ◽  
pp. 562-567 ◽  
Author(s):  
L. M. Brock ◽  
H. G. Georgiadis
Keyword(s):  
Steady State ◽  
Heat Source ◽  
Half Space ◽  
Constant Velocity ◽  
Characteristic Length ◽  
Surface Displacement ◽  
Contact Problems ◽  
Governing Equations ◽  
Asymptotic Expressions ◽  
Thermoelastic Characteristic

An asymptotic solution within the bounds of steady-state coupled thermoelastodynamic theory is given for the surface displacement and temperature due to a line mechanical/heat source that moves at a constant velocity over the surface of a half-space. This problem is of basic interest in the fields of contact mechanics and tribology, and an exact formulation is considered. The results may serve as a Green’s function for more general thermoelastodynamic contact problems. The problem may also be viewed as a generalization of the classical Cole-Huth problem and the associated Georgiadis-Barber correction. Asymptotic expressions are obtained by means of the two-sided Laplace transform, and by performing the inversions exactly. The range of validity of these expressions is actually quite broad, because of the small value of the thermoelastic characteristic length appearing in the governing equations.

FFT Thermoelastic Solutions for Moving Heat Sources

1997 ◽  
Vol 119 (1) ◽  
pp. 156-162 ◽  
Author(s):  
Y. Ju ◽  
T. N. Farris
Keyword(s):  
Heat Source ◽  
Frequency Domain ◽  
Hot Spot ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Heat Sources ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Pass Filter ◽  
Low Pass Filter

An analytical frequency domain solution is obtained using the spatial Fourier transform for thermal and thermoelastic fields due to an arbitrary heat source or thermal distribution moving at constant speed over the surface of an insulated, traction free elastic half space. Conversions between the space and frequency domains for the input and output are performed efficiently and robustly using FFT techniques. The method is validated by comparison to the analytical result for the moving line heat source in which it is shown that numerical evaluation of the analytical solution is problematic for large speeds or distances from the heat source. The utility of the method is illustrated on the constant patch moving heat source and discretely distributed multiple heat sources known as the “hot spot” problem. It is shown, through several examples, that the effect of hot spots on surface displacement and tangential stress is small. Finally, this conclusion is generalized by quantifying the frequency domain solution for the moving heat source problem as a low pass filter.

Thermodynamic behaviour of microstretch viscoelastic solids with internal heat source

2014 ◽  
Vol 92 (5) ◽  
pp. 425-434 ◽  
Author(s):  
Sunita Deswal ◽  
Renu Yadav
Keyword(s):  
Heat Source ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Epoxy Material ◽  
Mech Phys Solid

The dynamical interactions caused by a line heat source moving inside a homogeneous isotropic thermo-microstretch viscoelastic half space, whose surface is subjected to a thermal load, are investigated. The formulation is in the context of generalized thermoelasticity theories proposed by Lord and Shulman (J. Mech. Phys. Solid, 15, 299 (1967)) and Green and Lindsay (Thermoelasticity, J. Elasticity, 2, 1 (1972)). The surface is assumed to be traction free. The solutions in terms of displacement components, mechanical stresses, temperature, couple stress, and microstress distribution are procured by employing the normal mode analysis. The numerical estimates of the considered variables are obtained for an aluminium–epoxy material. The results obtained are demonstrated graphically to show the effect of moving heat source and viscosity on the displacement, stresses, and temperature distribution.

Uniform asymptotic expansions for oblate spheroidal functions I: positive separation parameter λ

1992 ◽  
Vol 121 (3-4) ◽  
pp. 303-320 ◽  
Author(s):  
T. M. Dunster
Keyword(s):  
Wave Equation ◽  
Half Plane ◽  
Positive Constant ◽  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Small Positive Constant ◽  
Separation Parameter ◽  
Oblate Spheroidal ◽  
Uniform Asymptotic Expansions

SynopsisUniform asymptotic expansions are derived for solutions of the spheroidal wave equation, in the oblate case where the parameter µ is real and nonnegative, the separation parameter λ is real and positive, and γ is purely imaginary (γ = iu). As u →∞, three types of expansions are derived for oblate spheroidal functions, which involve elementary, Airy and Bessel functions. Let δ be an arbitrary small positive constant. The expansions are uniformly valid for λ/u2 fixed and lying in the interval (0,2), and for λ / u2when 0<λ/u2 < 1, and when 1 = 1≦λ/u2 < 2. The union of the domains of validity of the various expansions cover the half- plane arg (z)≦ = π/2.

Sign in / Sign up

Export Citation Format

Share Document