• Geomechanics and Engineering
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• 제23권4호
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• pp.393-403
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• 2020

We design the Green-Naghdi model type III (GN-III) with widespread thermoelasticity for a thermoelectric half space using a memory-dependent derivative rule (MDD). Laplace transformations and state-space techniques are used in order to find the general solution for any set of limit conditions. A basic question of heat shock charging half space and a traction-free surface was added to the formulation in the present situation of a traveling heat source with consistent heating speed and ramp-type heating. The Laplace reverse transformations are numerically recorded. There are called the impacts of several calculations of the figure of the value, heat source spead, MDD parameters, magnetic number and the parameters of the ramping period.

• Structural Engineering and Mechanics
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• 제33권6호
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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.

• Geomechanics and Engineering
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• 제21권1호
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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.

• Steel and Composite Structures
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• 제25권2호
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• pp.177-186
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• 2017

In this work, the model of magneto-thermoelasticity based on memory-dependent derivative (MDD) is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The $Lam{\acute{e}}^{\prime}s$ modulii are taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. A numerical method is employed for the inversion of the Laplace transforms. The effects of the time-delay on the temperature, stress and displacement distribution for different linear forms of Kernel functions are discussed. Numerical results are represented graphically and discussed.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.507-519
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• 2019

The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

• Steel and Composite Structures
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• 제45권4호
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• pp.535-546
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• 2022

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

• Structural Engineering and Mechanics
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• 제34권3호
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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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• 제14권3호
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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.

• 대한기계학회논문집A
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• 제21권4호
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• pp.673-678
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• 1997

Stress wave propagations in an elastic half space to a normal point force of ramp type in time are analyzed. The governing equations are transformed by applying the Laplace and Hankel transforms with respect to time and radial distance. The inversion of Laplace transforms are performed by employing the Cagniard-de Hoop method, where the Rayleigh waves at surface are obtained by including the residue terms. The stress waves computed at the location very cose to the surface are shown to be almost identical to the surface waves obtained by the residue method except the Rayleigh wavefront. It is found that at the surface, the stresses are dominated by the Rayleigh waves, whose amplitudes increase linearly with time when time is very large. It is also found that in the interior part, the radial stress has a logarithmic singularity at the shear wavefront, while tangential stress shows no singularity.

• Steel and Composite Structures
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• 제18권4호
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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.