Hydrostatic Initial Stress Research Articles

Influence of Gravity and Hydrostatic Initial Stress on Wave Propagation in Context of Three Phase Lag Thermoelasticity

Influence of Gravity and Hydrostatic Initial Stress on Wave Propagation in Context of Three Phase Lag Thermoelasticity

Analysis of an initially stressed functionally graded thermoelastic medium (type III) without energy dissipation

The current investigation deals with the deformation of a non-homogeneous thermoelastic half space under hydrostatic initial stress for the Green–Naghdi model III. The medium is supposed to be rotating with a constant angular velocity. The non-homogeneous properties of the material are along the x-direction. At the first instance, the problem has been solved analytically to obtain stress and displacement components. Further, the numerical values of these expressions are evaluated using a computer program for a particular medium. The numerical values obtained are then presented graphically to show the effect of initial stress parameter and non-homogeneity parameter on the quantities.

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

Effect of Hydrostatic Initial Stress on a Rotating Half-Space in the Context of a Two-Relaxation Power-Law Model

The simple and refined Lord–Shulman theories, the simple and refined Green–Lindsay theories as well as the coupled thermoelasticity theory were all employed to investigate the deformation of a rotating thermoelastic half-space. The present medium is subjected to initial pressure, bounded by hydrostatic initial stress and rotation. A unified heat conduction equation is presented. The normal mode strategy is applied to get all analytical expressions of temperature, stresses, and displacements. Some outcomes are tabulated to validate the present refined theories with the simple and classical thermoelasticity theories. The effect of hydrostatic initial stress was investigated on all field quantities of the rotating thermoelastic half-space with and without initial pressure. Two- and three-dimensional plots are illustrated in the context of refined theories to discuss the behaviors of all variables through the coordinate axes. Some particular cases of special interest have been deduced from the present investigation.

Moore–Gibson–Thompson Stability Model in a Two-Temperature Photonic Semiconductor Excited Medium Affected by Rotation and Initial Stress

In this paper, the two-temperature theory is used to examine a novel model that generalizes the Moore–Gibson–Thompson (MGT) effect according to two-dimensional electronic/thermoelastic deformation. The main equations for a semiconductor medium in the context of the impact of rotation are explained in terms of the impact of the initial hydrostatic stress at the free surface. The normal-mode approach is used to derive the precise formulae for the fundamental physical quantities (i.e., normal displacement, normal load stress, electronic diffusion (carrier density), dynamic and conductive temperature distribution) under the influence of the two-temperature coefficient. The comparison with the base state is performed using linear stability analysis. To make some comparisons based on the various values of thermal memories, the influence of a number of novel parameters is applied to each of our primary physical quantities, such as the rotation parameter and the initial stress. An example of the main fields’ perturbation is also obtained and graphically described.

Waves propagation for magneto-thermoelastic medium during the two-temperature theory with the gravitational field

The interaction between the generalized thermoelasticity theory and two-temperature theory is studied in the context of the two-dimensional (2D) deformation processes of an elastic medium. The influences of the gravitational field, hydrostatic initial stress, and magnetic field are used during the problem discretion in the context of the Lord-Şhulman (L-S) theory, the Green-Naghdi theory of type III (G-N III), and the three-phase-lag model (3PHL). The general solutions are obtained when the interaction between different fields (gravity field and magnetic field) occurs. The harmonic vibration technique in the physical domain is used to obtain the main exact expressions (physical quantities) for the waves’ velocity and attenuation coefficients for (i) Stoneley waves, (ii) Love waves, and (iii) Rayleigh waves. Different types of boundary conditions, according to the heating processes, are taken into account. Comparisons are carried out according to the effect of relaxation times (three theories of thermoelasticity). The obtained results are calculated numerically and presented graphically with some comparisons in the absence and the presence of the gravity field, the hydrostatic initial stress, and the magnetic field.

Plasma-thermal-elastic waves of semiconductor induced by laser pulses with hydrostatic initial stress and the hyperbolic two-temperature theory

The hyperbolic two-temperature theory under the effect of initial stress is used to investigate the surface wave propagations on a semiconductor medium. The governing equations are taken under the impact of the photo-thermal theory during the photo-excitation transport processes under the initial stress. The semiconductor medium is affected on the outer surface by a pulsed laser. The main equations are studied when they are coupled between the photo-thermal theory and thermoelasticity theory in two-dimensional (2D) deformation. Some thermoelasticity models (Lord–Shulman (LS), Green–Lindsay (GL) and the classical dynamical coupled theory (CD)) with the effect of relaxation time are used. The analytical solutions are obtained when the combination processes between the hyperbolic two-temperature theory and photo-thermoelasticity theory under the impact of initial stress and pulsed laser are considered. The harmonic wave is used to attain exact expressions on the main physical fields under photo-excitation processes. The mechanical, thermal and recombination plasma loads are applied at the medium-free surface to get the complete solutions of the basic studied physical fields. Some comparisons are made between the three thermoelasticity models under the electrical impact of thermoelectric coupling parameter, and there are shown graphically and discussed.

Magneto-Thermoelasticity with Thermal Shock Considering Two Temperatures and LS Model

The present investigation is intended to demonstrate the magnetic field, relaxation time, hydrostatic initial stress, and two temperature on the thermal shock problem. The governing equations are formulated in the context of Lord-Shulman theory with the presence of bodily force, two temperatures, thermal shock, and hydrostatic initial stress. We obtained the exact solution using the normal mode technique with appropriate boundary conditions. The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates. The results obtained are agreeing with the previous results obtained by others when the new parameters vanish. The results indicate that the effect of magnetic field and initial stress on the conductor temperature, thermodynamic temperature, displacement and stress are quite pronounced. In order to illustrate and verify the analytical development, the numerical results of temperature, displacement and stress are carried out and computer simulated results are presented graphically. This study helpful in the development of piezoelectric devices.

Thermoelastic with photogenerated model of rotating microstretch semiconductor medium under the influence of initial stress

A novel theoretical mathematical-physics model is obtained when the microstretch properties of elastic semiconductor medium are taken into account. This model is investigated in the context of photo-excitation transport processes through the thermoelasticity theory. The new model can be called Microstretch-photo-thermoelasticity (MPT) theory. The MPT model is studied under the impact of hydrostatic initial stress. The carrier’s charge field (carrier density or plasma wave) appears due to optical excitation. In this model, the interaction between thermal–mechanical-plasma waves is obtained when the medium is in a rotating case. When the medium is linear, isotropic and homogenous, the two-dimensional (2D) elastic and electronic deformations governing equations are investigated. This is done while taking into account the microinertia of the medium particles. The basic physical variables are obtained using the mathematical plane harmonic wave technique to obtain the general solutions. The complete analytical solutions are solved when conditions from mechanical-thermal and plasma type act at the free surface of the medium. The silicon (Si) and Germanium (Ge) materials are used to make the numerical simulations. The numerical results are displayed graphically and discussed.

Developments in the Reflection of plane waves

The present paper deals with the reflection of plane waves from the free surface. In this paper, we discuss the relatable background of the reflection of plane waves. The basic equations for isotropic and homogeneous generalized thermo-elastic media under hydrostatic initial stress are discussed in the context of thermo-elasticity.

Wave propagation in a temperature rate-dependent semiconducting medium with hydrostatic initial stress

The aim of this paper is to investigate the effect of hydrostatic initial stress and temperature dependence of the modulus of elasticity on surface wave propagation in the semiconducting medium under photothermal theory. An infinite elastic half-space is overlying the infinite semiconducting medium and a mechanical force of constant magnitude is applied along with the interface. Surface wave solutions are used to solve the coupled plasma, thermal, and elastic wave equations. The effect of hydrostatic initial stress and temperature dependent properties have been studied and depicted graphically on the penetration depths of the waves and the components of stresses, displacement, temperature distribution and carrier density. It is observed that the effect of hydrostatic initial stress on the penetration depths is prominent in temperature independent semiconducting medium.

Thermal conductivity changes of photo-elastic semiconductor excited in gravitational field with hydrostatic initial stress and internal heat source

In this work, the effect of hydrostatic initial stress is studied with the exited semiconductor material. Electrons are exited at the free surface of the elastic semiconductor medium using the photo-thermal-elastic theory during the transport (diffusion) process. The thermal memories are due to the dual-phase-lag (DPL) relaxation times of the heat conduction equation with a novel model. In this model, the thermal conductivity is chosen as a linear dependent function of the thermal temperature impact which is variable. The effect of gravitational field is taken into account during the two-dimensional (2D) elastic deformation under the impact of an internal heat source. The Kirchhoff transformation mapping is used. The harmonic wave (normal mode) method is applied for the 2D governing equations to obtain the main physical fields analytically. Some thermal and mechanical forces are applied with other elastic-plasma conditions at the free surface of the semiconductor material to get the complete solutions. Some comparisons used a novel parameters which depend on the DPL model and the differences in the thermal conductivity parameters and they are illustrated graphically and discussed.

Surface waves in hygrothermoelastic half-space with hydrostatic initial stress

The present research article deals with the study of surface wave propagation in hygrothermoelastic medium with hydrostatic initial stress. The coupled wave equations in terms of displacement, temperature and moisture concentration are solved analytically. The values of the penetration depth of different waves are obtained and depicted graphically against frequency. To explore some interesting results, the authors have also discussed deformation in the medium caused due to a mechanical force along the free surface of hygrothermoelastic solid with hydrostatic initial stress. The components of displacement, mechanical stresses, moisture concentration and temperature distribution in the medium are obtained and presented analytically. The graphical results of the variations of these quantities are presented graphically to show the effect of hydrostatic initial stress.

Photothermal Excitation Process during Hyperbolic Two-Temperature Theory for Magneto-Thermo-Elastic Semiconducting Medium

A novel technique is used to study the magnetic field influence in the free surface of an elastic semiconductor medium for a one-dimensional (1D) deformation. The problem is formulated during the hyperbolic two-temperature theory to study the coupled between the plasma, thermo-elastic waves. The investigation is conducted during a photothermal transport processes with the effects of both initial hydrostatic stress and some mechanical force. Using the Laplace transform method, the governing equations of the elastic waves, carrier density, quasi-static electric field, heat conduction equation, hyperbolic two temperature coefficient and constitutive relationships are obtained for the thermo-magnetic-electric medium. The mechanical stresses, thermal and plasma boundary conditions are applied on the interface adjacent to the vacuum to obtain the basic physical quantities in Laplace domain. The inversion of Laplace transform with numerical method is applied to obtain the complete solutions in time domain for the main physical fields under investigation. The effects of thermoelectric, thermoelastic and hyperbolic two temperature parameters of the applied force on the displacement component, carrier density, force stress and temperature distribution have been discussed graphically.

Correction to: A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress

Correction to: A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress

Analytical solution of a rotating semiconductor elastic medium due to a refined heat conduction equation with hydrostatic initial stress

The semiconductor elastic medium in the context of the photothermal theory under the influence of rotation field is studied. A novel model of the governing equations is investigated due to the refined multi-phase-lags with the thermal relaxation times of the heat equation with the hydrostatic initial stress during transport process of the photothermal phenomenon. The interaction between the multi-waves of elastic-thermal-plasma is obtained. The normal mode method in the two dimensions is applied to obtain the exact solutions of the basic physical quantities under investigation. Plasma, thermal and mechanical loads have been applied on the free surface of the semi-infinite semiconductor elastic medium to get the complete solutions of the basic physical fields. Some comparisons are shown graphically and they are discussed as a function of thermal memories with the variation of some parameters. Silicon (Si) material is used to make the numerical simulation and to display the sensitivity to the variation of the rotation parameter.

Analytical solutions of time-fractional heat order for a magneto-photothermal semiconductor medium with Thomson effects and initial stress

The influence of hydrostatic initial stress in the context of the time-fractional heat order equation is investigated. The strong electromagnetic field is applied at the external surface of semiconductor elastic medium during the photothermal transport process. The Thomson influence appears due to the strong magnetic field. The behavior of wave propagations of the elastic medium is obtained in context of the thermoelectricity theory with initial stress. The governing main equations are taken in two dimensions to describe the interaction between elastic-thermal-plasma and electromagnetic waves for fractional cases. The density of charge is studied as a function of time only when the electric current is induced. The separation of variables is used as a mathematical technique to obtain the exact solutions of the distributions of physical quantities under investigation. Some mechanical, thermal, plasma and magnetic conditions are applied at the free surface elastic medium. A numerical simulation is used to obtain physical quantities distributions graphically and discussed theoretically in various fractional cases.

Electromagnetic and Thomson effects during photothermal transport process of a rotator semiconductor medium under hydrostatic initial stress

The effect of rotation and hydrostatic initial stresses during electromagnetic field which is fallen on the outer surface of semiconductor medium is studied. The Thomson influence in context of photo thermal excitation process is investigated. The thermoelectricity theory is applied explain the waves behavior in the elastic semiconductor homogenous, isotropic medium. The governing equations describe the overlapping between plasma, electro-magnetic and elastic waves in two dimensional deformations when the medium is in rotation. The induced electric current is studied only when the charge density is a function of time. The normal mode analysis is a mathematical method which is used to get the physical fields distributions under investigation. The mechanical forces, electromagnetic effects thermal loads and plasma diffusion recombination process are taken at the outer free surface of the medium to obtain the complete solutions. All distributions of waves of physical quantities are represented graphically and discussed under the influence of rotation, initial stresses and Thomson parameter.

The effect of gravity and hydrostatic initial stress with variable thermal conductivity on a magneto-fiber-reinforced

The present paper is concerned at investigating the effect of hydrostatic initial stress, gravity and magnetic field in fiber-reinforced thermoelastic solid, with variable thermal conductivity. The formulation of the problem applied in the context of the three-phase-lag model, Green-Naghdi theory with energy dissipation, as well as coupled theory. The exact expressions of the considered variables by using state-space approaches are obtained. Comparisons are performed in the absence and presence of the magnetic field as well as gravity. Also, a comparison was made in the three theories in the absence and presence of variable thermal conductivity as well as hydrostatic initial stress. The study finds applications in composite engineering, geology, seismology, control system and acoustics, exploration of valuable materials beneath the earth's surface.

An analytical solution for time-dependent stress field of lined circular tunnels using complex potential functions in a stepwise procedure

Time-dependent behavior of surrounding mass plays a significant role in designing underground constructions. Considering simple configuration of lined circular tunnels, a lot of solution have been proposed to this problem. However, many assume hydrostatic initial stress field, and other solutions are only applicable to simple rheological models and could not account for viscosity effect in long-term time periods. In this study, an analytical plane strain solution is proposed for lined circular tunnels under non-hydrostatic initial stress field, assuming rock mass as a viscoelastic material obeying Burgers model, while concrete lining is supposed to have linear elastic behavior. The solution which employs complex variable method combined with correspondence principle benefits from time discretization approach enabling the solution to take into account the viscosity effect in the both short-term and long-term periods of time, while predicting stress components accurately. The results obtained by the proposed solution were compared with those predicted by finite element COMSOL software which exhibited a close agreement. It was found that by increasing time both the proposed analytical solution and finite element numerical method tend to an oblique asymptote due to viscosity effect of Maxwell body in the Burgers model. Finally, a parametric analysis was performed with respect to Burgers model coefficients which showed different behavior for short and long periods of time.