Plane waves in generalized thermoelasticity

The properties of two dilatational motions in the context of generalized thermoelasticity are studied. The exact solution to the frequency equation is given and the exact values of the real and imaginary parts of the wave number are calculated. Approximate representations of this solution are derived for large and small frequencies, along with the ranges of validity. In this context the wave motions are unchanged for small frequencies, but both are modified at large frequencies. The major modifications concern only the thermal wave: the phase velocity approaches a constant value as frequency increases without limit; and the specific loss does not have any local extremum. Finally, the behaviour of amplitude ratios for small and large frequencies is discussed and the results obtained here are compared with those of earlier investigations in coupled thermoelasticity.     

On the plane strain in a generalized theory of thermoelasticity

This paper is concerned with the plane strain in the linear theory of generalized thermoelasticity, proposed by Green and Lindsay[1]. Using the associated matrices method[2], a representation of Galerkin type, is given. This representation is used to derive the solution of the vibration problem corresponding to concentrated body forces and concentrated heat source in an infinite medium.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags

The present paper deals with the investigation of the propagation of harmonic plane waves with assigned frequency by employing the thermoelasticity theory with dual-phase-lags (Tzou [7], Chandrasekharaiah [10]). The exact dispersion relation solutions for the plane wave are obtained analytically and asymptotic expressions of several characterizations of the wave fields, such as phase velocity, specific loss, penetration depth and amplitude ratios are obtained for both the high frequency as well as low frequency values. In order to illustrate the analytical results, the computational tool Mathematica is used to find the numerical values of different wave fields at intermediate values of frequency and results are depicted in different figures. A detailed analysis of the effects of phase-lags on plane wave is presented on the basis of analytical and numerical results and significant points are highlighted.     

On conservation laws in generalized dynamic thermoelasticity

The differential equations of generalized dynamic thermoelasticity constitute a coupled non-self-adjoint system of PDEs, which in its variational form does not admit a Lagrangian. However following exterior calculus methodology, we augment the space of dependent variables, accompanying the initial differential equations with suitable adjoint equations and additional auxiliary “fields”. So the construction of a Lagrangian is now possible along with the realization of Noether's theory for finding conservation laws. Finally, in our case, it is possible to characterize the additional dependent variables in terms of the physical fields themselves and obtain then conservation laws expressed via the original known thermoelastic fields.     

On fractional order generalized thermoelasticity with micromodeling

This paper presents the theory of fractional order generalized thermoelasticity with microstructure modeling for porous elastic bodies and synthetic materials containing microscopic components and microcracks. Built upon the micromorphic theory, the theory of fractional order generalized micromorphic thermoelasticity (FOGTE_mm) is firstly established by introducing the fractional integral operator. To generalize the FOGTE_mm theory, the general forms of the extended thermoelasticity, temperature rate dependent thermoelasticity, thermoelasticity without energy dissipation, thermoelasticity with energy dissipation, and dual-phase-lag thermoelasticity are introduced during the formulation. Secondly, the uniqueness theorem for FOGTE_mm is established. Finally, a generalized variational principle of FOGTE_mm is developed by using the semi-inverse method. For reference, the theories of fractional order generalized micropolar thermoelasticity (FOGTE_mp) and microstretch thermoelasticity (FOGTE_ms) and the corresponding generalized variational theorems are also presented.     

On electromagneto-thermoelastic plane waves

Summary The propagation of harmonically time-dependent electromagneto-thermoelastic plane waves of assigned frequency in an unbounded, homogeneous, isotropic, elastic, thermally and electrically conducting medium is considered. The theory of thermoelasticity recently proposed by Green and Lindsay is used to account for the interactions between the elastic and thermal fields. The results pertaining to phase velocity and attenuation coefficient of various types of waves are compared with those of Nayfeh and Nemat-Nasser who have dealt with a theory of thermoelasticity having a thermal relaxation time.

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Elektro-magnetothermoelastische ebene Wellen

Zusammenfassung Die Fortpflanzung von harmonischen, zeitabhängigen, elektro-magnetothermoelastischen ebenen Wellen von gegebener Frequenz in einem unbegrenzten, homogenen, isotropischen, elastischen, wärme- und elektrisch leitendem Material wird behandelt. Die Wechselwirkung zwischen den elektrischen und thermischen Feldern wird durch die kürzlich vorgeschlagene Thermoelastizitätstheorie von Green und Lindsay beschrieben. Die Dämpfungskoeffizienten der verschiedenen Wellentypen werden mit denen von Nayfeh und Nemat-Nasser verglichen, welche schon früher eine Thermoelastizitätstheorie mit thermischer Relaxationszeit behandelt hatten.

     

On a mixed problem for the temperature equation in generalized thermoelasticity

Summary In the context of the generalized thermoelasticity theory, a mixed problem for the temperature equation is constructed by starting with a mixed problem for the coupled governing equations for the displacement and temperature fields. The uniqueness of solution of the former problem is established. A method of deducing a solution of the latter problem from that of the former problem is presented.     

Growth and decay in generalized thermoelasticity

A theory of linear thermoelasticity has been proposed by Green and Lindsay [J. Elasticity 2 (1972) 1-7]. Using their theory we treat the thermoelastic problem for a semi-infinite cylinder where the lateral surface of the cylinder is held either at zero temperature and zero displacement, or at zero heat flux and zero traction. Growth and decay bounds for the energy are derived.     

On isovector fields and similarity solutions of generalized dynamic thermoelasticity

The purpose of the present work is the investigation of the isovector fields as well as the similarity solutions of the PDEs describing the generalized dynamic thermoelasticity. The adopted methodology and solution techniques belong totally to the analytical realm, while special treatment of the reduced differential equations resulting from similarity solution adoption has been realized.     

Some considerations on generalized thermoelasticity

In this paper the analysis is based on the decoupled field equations of generalized thermoelasticity. These equations have been solved with the help of integral transforms. The dynamic behaviour of an elastic half space due to a thermal shock on the boundary is also discussed. Because the “second sound” effects are short lived, the small time approximations have been considered. The displacement is continuous and temperature is discontinuous on both the elastic as well as thermal wave fronts.     

Variational theorem of generalized Cosserat-medium thermoelasticity

An equation which represents the content of the variational theorem of generalized Cosserat-medium elasticity is introduced. It is shown that, on the basis of this theorem, the basic energy equation of this medium may be obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 139–142, January, 1981.     

Equations of generalized thermoelasticity of cosserat medium

Dynamic equations of generalized thermoelasticity are derived for the Cosserat continuum, the theorem of uniqueness of solution of the problem is proved, and an expression is derived which represents the content of a theorem analogous to the reciprocal theorem.Notation absolute temperature - d surface element - Euler radius vector of a point - r Lagrange radius vector of a point - n vector of the external normal to the surface - E unit tensor - s entropy per unit volume - q vector of heat flux - w density of volumetric heat release - =(–_o) _o ¹ relative deviation of temperature from the initial value - _o initial absolute temperature of the medium - asymmetric strain tensor - tensor of flexure and torsion - _o constant characterizing the rate of heat propagation - k coefficient of thermal conductivity - A mechanical power of external surface forces - L mechanical power of external body forces - W kinetic energy of strain - potential energy of strain - X dissipation function - temperature potential - U thermal analog of the power of internal sources - Q thermal analog of the power of the surface of sources Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, Wo. 4, pp. 716–723, October, 1980.     

Size-dependent generalized thermoelasticity model for Timoshenko microbeams

A size-dependent, explicit formulation for coupled thermoelasticity addressing a Timoshenko microbeam is derived in this study. This novel model combines modified couple stresses and non-Fourier heat conduction to capture size effects in the microscale. To this purpose, a length-scale parameter as square root of the ratio of curvature modulus to shear modulus and a thermal relaxation time as the phase lag of heat flux vector are considered for predicting the thermomechanical behavior in a microscale device accurately. Governing equations and boundary conditions of motion are obtained simultaneously through variational formulation based on Hamilton’s principle. As for case study, the model is utilized for simply supported microbeams subjected to a constant impulsive force per unit length. A comparison of the results with those obtained by the classical elasticity and Fourier heat conduction theories is carried out. Findings indicate that simultaneous considering the length-scale parameter and thermal relaxation time has strong influence on the thermoelastic behavior of microbeams. In dynamic thermoelastic analysis of the microbeam, while the non-Fourier heat conduction model is employed, the modified couple stress theory predicts larger deflection compared with the classical theory.     

A generalized linear thermoelasticity theory for piezoelectric media

Summary A theory of thermoelasticity for piezoelectric materials which includes heat-flux among the independent constitutive variables is formulated. It is found that the linearized version of the theory admits a finite speed for thermal signals. An equation of energy balance and a theorem on the uniqueness of solution are obtained.     

On the representation of solutions for the theory of generalized thermoelasticity with three phase-lags

An analytical investigation on the plastic zone size (PZS) of a crack near a circular inclusion has been carried out. Both the crack and the circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, two stripe plastic zones at both crack tips are introduced. Using the solution of a circular inclusion interacting with a single dislocation as the Green’s function, the physical problem is formulated as a set of singular integral equations. With the aid of Erdogan and Gupta’s method and iterative numerical procedures, the singular integral equations are solved numerically for the PZS and the crack tip opening displacement. The results obtained in the current work can be reduced to those simpler cases of the Dugdale model.     

Response of frequency domain in generalized thermoelasticity with two temperatures

The paper is concerned with the time-harmonic deformation in a homogeneous, isotropic, generalized thermoelastic medium with two temperatures. The Hankel transform is employed to solve the boundary-value problem in the frequency domain in the context of two generalized theories of thermoelasticity (Lord and Shulman, Green and Lindsay). The inverse transform integral is evaluated by using the Romberg integration in order to obtain the results in the physical domain. The components of the stresses as well as the temperature and conductive temperature obtained in this manner are computed numerically. The effects of two temperatures are presented graphically.     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.