Different Theories Of Thermoelasticity Research Articles

Response of frequency domain in generalized thermoelastic medium under modified Green‐Lindsay with non‐local and two temperature

AbstractThis paper introduces a novel model for a generalized thermoelastic medium with homogeneity and isotropy, by applying the Modified Green‐Lindsay (MG‐L) theory of thermoelasticity. The focus is on analysing the deformation due to time‐harmonic by considering the impact of non‐local and two‐temperature (TT) parameters. The governing equations are solved using dimensionless quantities and a potential function. To address the boundary value problem in the frequency domain, the Hankel transform is employed. Specific boundary conditions, such as a normal force or thermal source, are applied. Analytical expressions for components of displacement, stresses, conductive temperature, and temperature distribution are derived in the transformed domain A numerical inversion technique is utilised to translate the solution into the physical domain. The study delves into exploring the influence of non‐local and two‐temperature parameters, as well as different theories of thermoelasticity on stresses, temperature distribution and conductive temperature. These effects are visually represented through graphical illustrations. Additionally, special cases of interest are examined and discussed.

Photothermal interactions in a semiconducting fiber‐reinforced elastic medium with temperature‐dependent properties under dual‐phase‐lag model

AbstractThis article highlights the study of photothermoelastic interactions in a semiconducting fiber‐reinforced anisotropic medium with temperature‐dependent properties. The model is studied in the context of the photothermal transport process with dual‐phase‐lag theory of generalized thermoelasticity. The governing equations describe the interactions between elastic and plasma thermal waves. The normal mode analysis is employed to procure the exact expressions of the physical fields under investigation. A mechanical load is applied at the outer free surface of the medium to obtain the complete solution of the displacements, stresses, temperature, and carrier density distributions. Numerical results are obtained and displayed graphically with the help of MATLAB software. Some special cases of interest have been deduced from the present study and comparisons are also made among the different theories of thermoelasticity.

Refined Green–Lindsay Model for the Response of Skin Tissue under a Ramp-Type Heating

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative thermoelasticity model. Thinner one-dimensional skin tissue is considered when its inner surface is free of traction and does not show any temperature increase. The skin tissue’s bounding surface has been heated by ramp-type heating. The classical thermoelastic theories are obtained from the present general formula. The governing equations of the present model are obtained. To move the system into a space state, the Laplace transform is used. The inverse of the Laplace transform is also used with Tzuo’s method to solve the problem. As a result, the field quantities are obtained numerically, and the results of the current model are graphically represented with a comparison to two different theories of thermoelasticity. The effects of various parameters on thermomechanical waves through the skin tissue are analyzed. The theory notes a vibrational behavior in heat transfer and a different effect on the parameters discussed in this article.

A Mathematical Study of a Semiconducting Thermoelastic Rotating Solid Cylinder with Modified Moore–Gibson–Thompson Heat Transfer under the Hall Effect

This research aims to investigate photo-thermoelastic interactions in a rotating infinite semiconducting solid cylinder under a high magnetic field acting along its axis with the Hall current effect. The boundary surface is subjected to a variable heat flux generated by an exponential laser pulse. The governing equations are expressed using a new photo-thermoelastic model generalized in the Moore–Gibson–Thompson photo-thermal (MGTPT) heat transfer model for a semiconducting medium. The Moore–Gibson–Thompson (MGT) equation is obtained by introducing a thermal relaxation parameter into the Green–Naghdi (GN III) model. The Laplace transform is utilized to determine the mathematical expressions for the components of displacement, carrier density, temperature field, and thermal stresses in the transformed domain. The numerical inversion technique is used to obtain the expressions in the physical domain. The impacts of thermal relaxations, different theories of thermoelasticity, the Hall current, and rotation on the displacement, temperature, thermal stresses, and carrier density are represented graphically using MATLAB software.

Transversely isotropic visco‐thermo‐elastic nanobeam with time harmonic laser pulse and new modified three phase lag Green‐Nagdhi model

AbstractThis investigation aims to examine the impact of the time‐harmonic laser pulse on the vibration phenomenon in 2D homogeneous transversely isotropic homogeneous visco‐thermoelastic nanobeam with a new modified three‐phase lag Green Nagdhi (TPL‐GN) model. The ends of the nanobeam are considered to be simply supported and held at a constant temperature. The mathematical model so formed is solved to derive the non‐dimensional expressions for lateral deflection, axial displacement, temperature distribution, axial stress, and thermal moment. Effect of frequency and viscosity with new modified TPL GN heat transfer is represented graphically for lateral deflection, axial displacement, temperature distribution, axial stress, and thermal moment using the MATLAB software. Comparisons are made with the different theories of thermoelasticity and visco‐thermoelasticity. Some particular cases are also deduced.

Fiber-reinforced magneto-thermoelastic composite material with hyperbolic two-temperature, fractional-order three-phase lag and new modified couple stress theory

The paper aims to study the new modified couple stress theory in fiber-reinforced magneto-thermoelastic medium (FrMTM) with Hall current, rotation and with hyperbolic two-temperature (H2T) due to ramp-type heat. The Fourier’s law of heat conduction with fractional-order (Fo) three-phase lag (TPL) derivative is used to form the model of the problem. Laplace and Fourier’s transforms are used to solve this mathematical model. The displacement components, temperature change, couple stress and axial stress components are calculated in the transformed domain and have been converted in the physical domain with the numerical inversion technique. These physical quantities are drawn graphically using the MATLAB software to show the effects of the FoTPL theory for different values of fractional-order parameter and different theories of thermoelasticity, namely, the FoTPL theory, the FoGN-III theory, the FoGN-II theory and the FoTPLGN-II theory.

New analytical method for dynamic response of thermoelastic damping in simply supported generalized piezothermoelastic nanobeam

AbstractThe present paper deals with the application of one‐dimensional piezoelectric materials in particular piezo‐thermo‐elastic nanobeam in the context of generalized piezothermoelastic theory. The ends of the nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non‐dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping, and frequency shift. Effect of frequency on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with different theories of thermoelasticity.

Plane Waves in Thermo-Viscoelastic Material with Voids Under Different Theories of Thermoelasticity

Propagation of time harmonic plane waves in an infinite thermo-viscoelastic material with voids has been investigated within the context of different theories of thermoelasticity. The equations of motion developed by Iesan [1] have been extended to incorporate the Lord-Shulman theory (LST) and Green-Lindsay theory (GLT) of thermoelasticity. It has been shown that there exist three coupled dilatational waves and an uncoupled shear wave propagating with distinct speeds. The presence of thermal, viscosity and voids parameters is responsible for the coupling among dilatational waves. All the existing waves are found to be dispersive and attenuated in nature. The phase speeds and attenuation coefficients of propagating waves are computed numerically for a copper material and compared under different theories of thermo-elasticity. The expressions of energies carried along each wave have also been derived. All the computed numerical results have been depicted through graphs. It is found that the influence of CT and GLT is almost same on wave propagation, while LST influences the wave propagation differently.

On Propagation of Rayleigh Type Surface Wave in Five Different Theories of Thermoelasticity

The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.

Thermo-viscoelastic materials with fractional relaxation operators

The new model of linear thermo-viscoelasticity for isotropic media taking into consideration the rheological properties of the volume with fractional relaxation operators is given. The governing equations are taken in a unified system from which some essential theorems on the linear coupled and generalized theories of thermo-viscoelasticity can be easily obtained. The resulting formulation is applied to several concrete problems, a thermal shock problem and a problem for a half-space subjected to ramp-type heating as well as a problem of a layer media. Laplace transform techniques are used. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effect of fractional relaxation operators and ramping parameter of heating with different theories of thermoelasticity.

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

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<sub>1</sub>, S<sub>2</sub>) 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.

Propagation of Rayleigh waves in magneto-thermo-elastic half-space of a homogeneous orthotropic material under the effect of rotation, initial stress and gravity field

The propagation of magneto-thermoelastic plane waves in an initially stressed, homogeneous orthotropic, conducting half-space under a magnetic field, rotation and gravity field have been investigated. The generalized theory of thermoelasticity is employed, by assuming the mechanical behavior as dynamic, to study the problem. The Lame’s potential is used to obtain the frequency equation that determines the velocity of Rayleigh waves that obtained as a real part and the attenuation coefficient as an imaginary part under the rotation, magnetic field, initial stress and gravity field. Numerical results have been given and illustrated graphically for each case considered. Dispersion curves of wave propagation are represented graphically in different theories of thermoelasticity. The results indicate that the effect of rotation, initial stress and gravity field are very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation, initial stress and gravity field.

Fractional Order Generalized Thermo-Piezoelectric Semi-Infinite Medium with Temperature-Dependent Properties Subjected to a Ramp-Type Heating

The generalized thermoelasticity theory that, based on a fractional order model, is used to solve a one-dimensional boundary value problem of a semi-infinite piezoelectric medium. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. The generalized thermo-piezoelectricity model in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The Laplace transform technique is used to obtain the general solution for any set of boundary conditions. The inverse Laplace transforms are numerically computed using the Fourier expansion techniques. The effects of fractional order and the ramping of heating parameters are studied and comparison with different theories of thermoelasticity are considered. The results are also compared to results obtained in the case of a temperature-independent modulus of elasticity.

Effect of Rotation on Rayleigh—Lamb Waves in an Isotropic Generalized Thermoelastic Diffusive Plate

The present investigation is aimed at studying the effect of rotation on propagation of Rayleigh—Lamb waves in a homogeneous isotropic thermoelastic diffusive plate of finite width in the framework of different theories of thermoelasticity, including the Coriolis and centrifugal forces. The medium is subjected to stress-free, thermally insulated, isothermal, and chemical potential boundary conditions and is rotating about an axis perpendicular to its plane. Secular equations corresponding to the symmetric and skew-symmetric modes of the plate are derived. Phase velocities and attenuation coefficients of various possible modes of wave propagation are computed from the secular equations. Amplitudes of displacements, temperature, and concentration for symmetric and skew-symmetric modes of plate vibrations are computed numerically. The computed results are presented graphically.

Bending Analysis of Functionally Graded Plates in the Context of Different Theories of Thermoelasticity

The quasistatic bending response is presented for a simply supported functionally graded rectangular plate subjected to a through‐the‐thickness temperature field under the effect of various theories of generalized thermoelasticity, namely, classical dynamical coupled theory, Lord and Shulman′s theory with one relaxation time, and Green and Lindsay′s theory with two relaxation times. The generalized shear deformation theory obtained by the first author is used. Material properties of the plate are assumed to be graded in the thickness direction according to a simple exponential law distribution in terms of the volume fractions of the constituents. The numerical illustrations concern quasistatic bending response of functionally graded square plates with two constituent materials are studied using the different theories of generalized thermoelasticity

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

The aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.

A Problem on Thermoelastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermoelasticity III

The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely: the extended thermoelasticity proposed by Lord and Shulman [2], the thermoelasticity without energy dissipation (Green and Nagdhi [3]) and thermoelasticity with energy dissipation (thermoelasticity type III [1]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained from different models of generalized thermoelasticity.

Free vibration of microstretch thermoelastic plate with one relaxation time

The propagation of waves in microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Lord and Shulman (L–S) theories of thermoelasticity. The secular equations for both symmetric and skew-symmetric wave mode propagation have been obtained. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation. The amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew symmetric wave modes are computed analytically and presented graphically for different theories of thermoelasticity. The theoretical and numerical computations are found to be in close agreement.

Effect of rotation on Rayleigh–Lamb waves in magneto-thermoelastic media

In this paper propagation of magnetic-thermoelastic plane waves in an initially unstressed, homogeneous isotropic, conducting plate, rotating about the normal to its faces with uniform angular velocity, under the action of uniform magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behavior as quasi-static and the mechanical behavior as dynamic, to study the problem. The secular equations for both symmetric and skew symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) modes of wave propagation gets decoupled from rest of the motion here, however it may not be in general possible if the rotation took place in an arbitrary direction. These waves propagate without the influence of temperature change and thermal relaxation time. At short wavelength limits, the secular equations for symmetric and skew symmetric modes reduce to Rayleigh surface wave frequency equation. Thin plate results are also deduced. Finally, the dispersion curves are computed and represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically, computed numerically at the end and plotted graphically. The result in case of non-rotating media, elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.

Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating

In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating. The inverse Fourier transforms are obtained analytically while the inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating with different theories of thermoelasticity.