© 1992 by Oxford University Press
LINEAR DYNAMICAL STABILITY IN CONSTRAINED THERMOELASTICITY I. DEFORMATION-TEMPERATURE CONSTRAINTS
( School of Mathematics, University of East Anglia Norwich NR4 7TJ )
Equations are derived governing an infinitesimal disturbance of a uniform equilibrium state Be of an unbounded body composed of a heat-conducting elastic material subject to a constraint linking the deformation and the temperature. No restriction is placed on the symmetry of the material and the freedom of choice of Be allows the presence of an arbitrary homogeneous prestrain. The stability of Be, in the context of linearized dynamics, is examined by studying the nature of plane-harmonic-wave solutions of the governing equations. It is found that, under very mild restrictions on the relevant material constants in Be, at least one of the four modes of wave propagation is always unstable, a conclusion which seriously undermines the legitimacy of the assumed type of constraint. The particular case of incompressibility at uniform temperature has been discussed by previous authors and is recapitulated here. Finally, an explanation of the inherent instability is provided by treating the constraint as a limit.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  V. Salnikov and N. Scott Thermoelastic Waves in a Constrained Isotropic Plate: Incompressibility at Uniform Entropy Mathematics and Mechanics of Solids, August 1, 2007; 12(4): 385 - 402. [Abstract] [PDF]
|
|
|
|
 |
|
 V. Salnikov and N. Scott Thermoelastic waves in a constrained isotropic plate: incompressibility at uniform temperature Q J Mechanics Appl Math, August 1, 2006; 59(3): 359 - 375. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. J. Leslie and N. H. Scott Wave Stability for Constrained Materials in Anisotropic Generalized Thermoelasticity Mathematics and Mechanics of Solids, October 1, 2004; 9(5): 513 - 542. [Abstract] [PDF]
|
|
|
|
|
|
J. Dunwoody and R. W. Ogden On the Thermodynamic Stability of Elastic Heat-Conducting Solids Subject to a Deformation--Temperature Constraint Mathematics and Mechanics of Solids, June 1, 2002; 7(3): 285 - 306. [Abstract] [PDF]
|
|
|
|
|
|
D. J. Leslie and N. H. Scott Wave Stability for Near-Incompressibility at Uniform Temperature or Entropy in Generalized Isotropic Thermoelasticity Mathematics and Mechanics of Solids, June 1, 2000; 5(2): 157 - 202. [Abstract] [PDF]
|
|
|
|
|
|
D. J. Leslie and N. H. Scorr Near Incompressibility at Uniform Temperature or Entropy in Isotropic Thermoelasticity Mathematics and Mechanics of Solids, September 1, 1998; 3(3): 243 - 275. [Abstract]
|
|
|
|
|
|
J. Casey and S. Krishnaswamy A Characterization of Internally Constrained Thermoelastic Materials Mathematics and Mechanics of Solids, March 1, 1998; 3(1): 71 - 89. [Abstract]
|
|