• Geomechanics and Engineering
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• v.21 no.1
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• pp.85-93
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• 2020

In this article, the generalized thermoelastic theory with fractional derivative is presented to estimate the variation of temperature, the components of stress, the components of displacement and the changes in volume fraction field in two-dimensional porous media. Easily, the exact solutions in the Laplace domain are obtained. By using Laplace and Fourier transformations with the eigenvalues method, the physical quantities are obtained analytically. The numerical results for all the physical quantities considered are implemented and presented graphically. The results display that the present model with the fractional derivative is reduced to the Lord and Shulman (LS) and the classical dynamical coupled (CT) theories when the fractional parameter is equivalent to one and the delay time is equal to zero and respectively.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.697-708
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• 2009

Stresses are solved for two parallel cracks in an infinite orthotropic plate during passage of incoming shock stress waves normal to their surfaces. Fourier transformations were used to reduce the boundary conditions with respect to the cracks to two pairs of dual integral equations in the Laplace domain. To solve these equations, the differences in the crack surface displacements were expanded to a series of functions that are zero outside the cracks. The unknown coefficients in the series were solved using the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors were defined in the Laplace domain and were inverted numerically to physical space. Dynamic stress intensity factors were calculated numerically for selected crack configurations.

• Steel and Composite Structures
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• v.34 no.2
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• pp.309-319
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• 2020

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic medium with mass diffusion and with two temperatures due to a thermal source and mechanical force. Laplace and Fourier transform techniques are applied to obtain the solutions of the governing equations. The displacements, stress components, conductive temperature, mass concentration and couple stress are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Isothermal boundary and insulated boundaryconditions are used to investigate the problem. Some special cases of interest are also deduced.

• Coupled systems mechanics
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• v.11 no.5
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• pp.459-483
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• 2022

In the present work, a new photothermoelastic model based on Moore-Gibson-Thompson theory has been constructed. The governing equationsfor orthotropic photothermoelastic plate are simplified for two-dimension model. Laplace and Fourier transforms are employed after converting the system of equations into dimensionless form. The problem is examined due to various specified sources. Moving normal force, ramp type thermal source and carrier density periodic loading are taken to explore the application of the assumed model. Various field quantities like displacements, stresses, temperature distribution and carrier density distribution are obtained in the transformed domain. The problem is validated by numerical computation for a given material and numerical obtained results are depicted in form of graphs to show the impact of varioustheories of thermoelasticity along with impact of moving velocity, ramp type and periodic loading parameters. Some special cases are also explored. The results obtained in this paper can be used to design various semiconductor elements during the coupled thermal, plasma and elastic wave and otherfieldsin thematerialscience, physical engineering.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.469-476
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• 2022

A mathematical model of Lord-Shulman photo-thermal theorem induced by pulse heat flux is presented to study the propagations waves for plasma, thermal and elastic in two-dimensional semiconductor materials. The medium is assumed initially quiescent. By using Laplace-Fourier transforms with the eigenvalue method, the variables are obtained analytically. A semiconductor medium such as silicon is investigated. The displacements, stresses, the carrier density and temperature distributions are calculated numerically and clarified graphically. The outcomes show that thermal relaxation time has varying degrees of effects on the studying fields.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.285-300
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• 2010

The two-dimensional deformation of a homogeneous, isotropic thermoelastic half-space with voids with variable modulus of elasticity and thermal conductivity subjected to thermomechanical boundary conditions has been investigated. The formulation is applied to the coupled theory(CT) as well as generalized theories: Lord and Shulman theory with one relaxation time(LS), Green and Lindsay theory with two relaxation times(GL) Chandrasekharaiah and Tzou theory with dual phase lag(C-T) of thermoelasticity. The Laplace and Fourier transforms techniques are used to solve the problem. As an application, concentrated/uniformly distributed mechanical or thermal sources have been considered to illustrate the utility of the approach. The integral transforms have been inverted by using a numerical inversion technique to obtain the components of displacement, stress, changes in volume fraction field and temperature distribution in the physical domain. The effect of dependence of modulus of elasticity on the components of stress, changes in volume fraction field and temperature distribution are illustrated graphically for a specific model. Different special cases are also deduced.

• Journal of electromagnetic engineering and science
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• v.14 no.3
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

• Steel and Composite Structures
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• v.18 no.4
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• pp.909-924
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• 2015

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.117-131
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• 2021

The problem of generalized thermoelasticity of two-temperature for finite piezoelectric rod will be modified by applying three different types of heating applications namely, thermal shock, ramp-type heating and harmonically vary heating. The solutions will be derived with direct approach by the application of Laplace transform and the Caputo-Fabrizio fractional order derivative. The inverse Laplace transforms are numerically evaluated with the help of a method formulated on Fourier series expansion. The results obtained for the conductive temperature, the dynamical temperature, the displacement, the stress and the strain distributions have represented graphically using MATLAB.