Basic Properties of Plane Harmonic Waves in a Prestressed Heat-Conducting Elastic Material

wick, P. Chad

doi:10.1080/01495737908962401

Cited by 58 publications

(45 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…is the referential thermal conductivity tensor, see Chadwick [17]. But in B we may have ¹ "¹ (X) so that G O0 and the heat #ux Q is non-vanishing, unlike that in (3.7).…”

Section: The Displacement-temperature Form Of the Xeld Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Thermoelasticity with thermomechanical constraints

Scott

2001

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

Equations are derived governing the behaviour of small disturbances superimposed on an underlying equilibrium con"guration of a thermoelastic body. The body may be materially inhomogeneous, non-homogeneously prestrained and be subjected to a non-uniform temperature resulting in non-constant-coe$cient partial di!erential equations. These equations are generalized to the case where thermomechanical constraints are present, both deformation-temperature and deformation-entropy constraints. It is known that the "rst of these types of constraints leads to material instabilities and the second does not. By examining nearly constrained materials, and taking an appropriate limit, we "nd that the instabilities associated with deformation-temperature constraints arise because the heat capacity at constant deformation becomes negative whilst deformation-entropy constraints are stable because the same heat capacity remains positive, though tending to zero in the limit of the constraint holding exactly. The ten important moduli of thermoelasticity are examined in the limit of each constraint holding exactly. It is found, for example, that for each type of constraint the heat capacity at constant stress remains positive and bounded away from zero. Results on wave propagation are also presented.

show abstract

“…is the referential thermal conductivity tensor, see Chadwick [17]. But in B we may have ¹ "¹ (X) so that G O0 and the heat #ux Q is non-vanishing, unlike that in (3.7).…”

Section: The Displacement-temperature Form Of the Xeld Equationsmentioning

confidence: 99%

“…Eqs. (4.8) and (4.9) are replaced by 17) so that the balance equations (3.36), taken in the form (4.18) lead to the "eld equations…”

Section: The Deformation-temperature Constraint F (F ¹)"0mentioning

confidence: 99%

Thermoelasticity with thermomechanical constraints

Scott

2001

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

show abstract

“…The matrix differen-90 tial operator adj M and the scalar differential operator det M are both well-defined as neither involves division by a differential operator. We need to make (2.4) more convenient by determining an explicit form for the differential operator det M. The method follows that of Chadwick (1979) in the harmonic plane wave case. By applying elementary methods to row 4 of M, we find that…”

Section: Reduction To a Single Equation In One Variablementioning

confidence: 99%

“…All other quantities occurring in (1.2) are 60 constants evaluated in the reference configuration: T is the ambient absolute temperature, ρ the mass density, c the specific heat and β i j , k i j andc i jkl are the components of the temperature coefficient of stress, conductivity and isothermal elasticity tensors, respectively. The last four quantities are defined by Chadwick (1979). The specific heat is positive and these tensors are positive definite.…”

Section: Introduction and Basic Equationsmentioning

confidence: 99%

Thermoelasticity and generalized thermoelasticity viewed as wave hierarchies

Scott

2007

IMA Journal of Applied Mathematics

View full text Add to dashboard Cite

It is seen how to write the standard form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This equation, of diffusive type, is of the eighth order in the space derivatives and seventh order in the time derivatives and so is parabolic in character. After having seen how to cast the 1D diffusion equation into Whitham's wave hierarchy form, it is seen how to recast the full equation, for unidirectional motion, in wave hierarchy form. The higher order waves are isothermal and the lower order waves are isentropic or purely diffusive. The wave hierarchy form is then used to derive the main features of the solution of the initial-value problem, thereby bypassing the need for an asymptotic analysis of the integral form of the exact solution. The results are specialized to the isotropic case. The theory of generalized thermoelasticity associates a relaxation time with the heat flux vector and the resulting system of equations is hyperbolic in character. It is also seen how to write this system in wave hierarchy form which is again used to derive the main features of the solution of the initial-value problem. Simpler results are obtained in the isotropic case.

show abstract

“…El-Karamany and Ezzat (2011) introduced two models where the fractional derivatives and integrels are used to modify the Cattaneo heat conduction law (1958) and in the context of two temperature thermoelasticity theory, uniqueness and reciprocity theorems are proved, the convolution principle is given and is used to prove a uniqueness theorem with no restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions. Chadwick and Sheet (1970) and Chadwick (1979) discussed propagation of plane harmonic waves in transversely isotropic and homogeneous anisotropic heat conduction solids respectively. Banerjee and Pao (1974) studied the thermoelastic waves in anisotropic solids.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness, reciprocity theorems and plane wave propagation in different theories of thermoelasticy

Kumar¹,

Gupta²

2013

International Journal of Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this work, a compact form of different theories of thermoelasticity is considered. The governing equations for particle motion in a homogeneous isotropic thermoelastic medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in a homogeneous isotropic thermoelastic medium is studied. For a three dimensional problem there exist four waves, namely a P-wave, two transverse waves (S 1 , S 2 ) and a thermal wave (T). From the obtained results the different characteristics of waves such as the phase velocity and attenuation coefficient are computed numerically and presented graphically. Some special cases are also discussed.

show abstract

Basic Properties of Plane Harmonic Waves in a Prestressed Heat-Conducting Elastic Material

Cited by 58 publications

References 12 publications

Thermoelasticity with thermomechanical constraints

Thermoelasticity with thermomechanical constraints

Thermoelasticity and generalized thermoelasticity viewed as wave hierarchies

Uniqueness, reciprocity theorems and plane wave propagation in different theories of thermoelasticy

Contact Info

Product

Resources

About