Generalized Plane Waves in a Rotating Thermoelastic Double Porous Solid

The present investigation is to study the plane problem in initially stressed thermoelastic half-space with voids due to thermal source. Lord-Shulman (Lord and Shulman 1967) theory of thermoelasticity with one relaxation time has been used to investigate the problem. A particular type of thermal source has been taken as an application of the approach. Finite element technique has been used to solve the problem. The components of displacement, stress, temperature change and volume fraction field are computed numerically. The resulting quantities are depicted graphically for different values of initial stress parameter. The relaxation time and the initial stress parameter have a significant effect on all distributions.

PurposeThe purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.Design/methodology/approachThe paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.FindingsThe paper finds the fundamental solution of partial differential equations in terms of elementary functions.Originality/valueAssuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

A study is made of the propagation of time‐harmonic magneto‐thermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of Kelvin‐Voigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The generalized thermoelasticity theory of type II (Green and Naghdi model) is used to study the propagation of waves. A more general dispersion equation for coupled waves is derived to ascertain the effects of rotation, finite thermal wave speed of GN theory, viscoelastic parameters and the external magnetic field on the phase velocity, the attenuation coefficient, and the specific energy loss of the waves. Limiting cases for low and high frequencies are also studied. In absence of rotation, external magnetic field, and viscoelasticity, the general dispersion equation reduces to the dispersion equation for coupled thermal dilatational waves in generalized thermoelasticity II (GN model), not considered before. It reveals that the coupled thermal dilatational waves in generalized thermoelasticity II are unattenuated and nondispersive in contrast to the thermoelastic waves in classical coupled thermoelasticity (Chadwick (1960)) which suffer both attenuation and dispersion.

In this article, a two-dimensional problem is studied in a homogeneous isotropic thermoelastic medium with double porosity in the context of nonlocal thermoelasticity and the problem is treated in the presence of the Green–Naghdi model of type-III. Constitutive relations and field equations are derived and the state space approach is employed to solve this problem. Thermal shock is applied on the boundary of the surface. From these relations and expressions, we have calculated stress components, displacement components, and temperature for different values of distance and time numerically and plotted graphically to demonstrate and compare theoretical results. The influences of void parameters, locality, and nonlocality on the various physical quantities are also analyzed. Some particular and special cases are also deduced from this study and compared with the existing results.

Free vibration of microstretch thermoelastic plate with one relaxation time

An extended Kalman filter is modified to support only magnetometer data as a measurement for spacecraft attitude information. Actual on-orbit data from a student satellite is used in the filter from three different time periods and varying data frequencies. The extended Kalman filter has a thermal model that utilizes external temperature data as a verification tool for filter convergence and for parameter tuning. It can capture the frequency of temperature changes and the correct side panel being lit by the sun as long as the filter converges properly, but not the magnitude of the temperature at a specific time. A solar panel power model is also attempted, which was found to be unusable due to power budget issues and the side panel current sensors railing. Convergence of the three sets of data showed that a 30 second snapshot rate converges to a more accurate attitude information when the satellite has a 0.1 rev/min rotation rate compared to the 1.0 rev/min rotation rate data. A 10 second snapshot rate gives more accurate attitude information for data from a satellite with a 1.0 rev/min rotation rate. By investigating the drastic reduction in the satellite’s rotation rate over 6 months, it was discovered that the satellite’s antenna is most likely magnetized, causing it to try to align itself with the Earth’s magnetic field, slowing down the rotation rate of the satellite from 1 rev/min to 0.1 rev/min.

This manuscript investigates the disruptions occurring in a two-dimensional homogeneous, isotropic, thermoelastic medium with diffusion, double porosity and microtemperatures under Lord and Shulman (LS) theory of generalized thermoelasticity. A mechanical load is applied at the outer free surface of the solid half-space. To procure the exact expressions for various field variables, normal mode analysis is utilized. Numerical computations are performed for a particular material and the acquired results are visualized through graphical representations with the aid of MATLAB software. Comparisons are carried out to elucidate the influences of diffusion parameter, time, double porosity and intensity of load on the resulting quantities. 2010 MSC: 74A15, 80A20.

In this study, the identification of thermoelastic mass diffusion was examined on a homogeneous isotropic microstretch thermoelastic diffusion (HIMTD) solid due to normal force on the surface of half space. In the framework of Cartesian symmetry, the components of displacement, stresses, temperature change, and microstretch as well as couple stress were investigated with and without microstretch and diffusion. The expression of the field functions was obtained using the Laplace and Fourier transforms. So as to estimate the nature of the components of displacement, stresses, temperature change, and microstretch as well as couple stress in the physical domain, an efficient approximate numerical inverse Laplace and Fourier transform technique and Romberg’s integration technique was adopted. It was meticulously considered and graphically illustrated how mass diffusion and microstretch affect thermoelastic deformation. Our objective was to address the inquiry regarding the impact of thermoelastic mass diffusion and microstretch on the field functions in the presence of a mass concentration source within the medium. Specifically, we aimed to investigate how these phenomena amplify the aforementioned effect.

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which are defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite solid with void under the action of an induced magnetic field due to the presence of a prescribed plane heat source. The heat transport equation for this problem is involving the memory-dependent derivative on a slipping interval in the context of Lord Shulman model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature and deformations are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of a magnetic field also.

On the propagation of Lamb waves in viscothermoelastic plates under fluid loadings

This study investigates the two-dimensional behavior of a nonlocal micropolar double-porous thermoelastic material with voids (MDPTMWV) within the framework of the Moore–Gibson–Thompson (MGT) theory. An isotropic, homogeneous, initially stressed, rotating thermoelastic half-space with double porosity is considered. The MGT heat conduction model, incorporating memory-dependent derivatives and variable thermal conductivity, is employed. Governing equations are derived using generalized thermoelasticity, and analytical solutions for displacement, temperature, equilibrated stress, and thermal stress components are obtained via Lame’s potentials combined with normal mode analysis. The model is analyzed under boundary conditions including variable temperature, normal stress, constant equilibrated stress, and stress-free surfaces. Numerical evaluations using MATHEMATICA illustrate the effects of time, rotation, initial stress, and nonlocal parameters. The results indicate that double porosity and the considered parameters significantly amplify material responses, particularly under increasing time, rotation, initial stress, and nonlocal effects. Several special cases are discussed and validated against the literature. These findings provide insights relevant to geophysics, seismology, and earthquake engineering.

Based upon Green–Naghdi thermoelastic theory of type II (without energy dissipation), the transient thermoelastic responses of a semi-infinite fiber-reinforced porous body are investigated with the initial stress considered. The surface is subjected to a zonal time-dependent thermal shock. The solution to the problem is obtained by solving finite element governing equations, from which the transient thermoelastic responses, i.e., temperature, stresses, displacements, as well as the change in volume fraction field, are presented graphically. The effect of fiber reinforcement and the initial stress is discussed. It is observed that the fiber reinforcement and initial stress have no influence on temperature, while have great influences on the stresses, the change in the volume fraction field and displacements. This work may provide theoretical basis and meaningful suggestions for designing various fiber-reinforced anisotropic structures with voids.

The present research deals in two dimensional (2D) transversely isotropic magneto generalized thermoelastic solid without energy dissipation and with two temperatures due to time harmonic sources in Lord-Shulman (LS) theory of thermoelasticity. The Fourier transform has been used to find the solution of the problem. The displacement components, stress components and conductive temperature distribution with the horizontal distance are calculated in transformed domain and further calculated in the physical domain numerically. The effect of two temperature are depicted graphically on the resulting quantities.

The present research deals in two dimensional transversely isotropic magneto thermoelastic solid with rotation due to time-harmonic source in generalised Lord-Shulman (LS) theory of thermoelasticity. The Fourier transform has been used to find a solution to the problem. The displacements components, stress components, and conductive temperature distribution with the horizontal distance in the physical domain are calculated numerically. The effect of rotation and various frequencies with two temperature (WTT) are depicted graphically on the resulting quantities. The proposed model is helpful for finding the type of relations between mechanical and thermal fields as most of the structural elements of heavy industries are frequently related to mechanical and thermal stresses at a higher temperature.

A new model for the simulation of moisture and thermal diffusivity in a semiconducting solid cylinder according to the Moore-Gibson-Thompson-Photo-Thermal (MGTPT) theory of thermoelasticity has recently been presented. The purpose of this study is to investigate the photo-thermoelasticity of an infinite semiconducting solid cylinder rotating with the boundary surface being subjected to a laser pulse with variable heat flux. For this purpose, the mathematical model is solved by using the Laplace transform technique in the transformed domain. The numerical inversion of the mathematical model yields all the physical parameters in the physical domain, such as displacement components, thermal stresses, and carrier densities. To clearly illustrate the effects of reference moisture, a graphic representation of all these parameters is generated by using the MATLAB software. The results of this study will be useful in further enhancing the behavior of semiconductors under these dynamic loading conditions and hence, improve their performance in various applications.Thus, the model provides an effective way to model the moisture and thermal diffusivities of the solid cylinder to better understand phenomena occurring in a broad range of semiconductor devices and more effectively design them.