• Advances in materials Research
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• 제7권3호
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• pp.203-220
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• 2018

This investigation is focused on the study of effect of hall current in transversely isotropic magneto thermoelastic homogeneous medium with fractional order heat transfer and rotation. As an application the bounding surface is subjected to normal force. The research becomes more interesting due to interaction of Hall current with the effect of rotation as it has found various applications. Laplace and Fourier transform is used for solving field equations. The analytical expressions of temperature, displacement components, stress components and current density components are computed in the transformed domain. The effects of hall current and fractional order parameter at different values are represented graphically.

• Steel and Composite Structures
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• 제38권2호
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• pp.213-221
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• 2021

The objective of this paper is to study the deformation in a homogeneous isotropic thermoelastic solid using modified couple stress theory subjected to ramp-type thermal source with two temperature. The advantage of this theory is the involvement of only one material length scale parameter which can determine the size effects. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The components of displacement, conductive temperature, stress components and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effect of two temperature is depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the size effects of microstructures.

• Steel and Composite Structures
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• 제38권5호
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• pp.523-531
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• 2021

The generalized thermoelastic analysis problem of a two-dimension porous medium with and without energy dissipation are obtained in the context of Green-Naghdi's (GNIII) model. The exact solutions are presented to obtain the studying fields due to the pulse heat flux that decay exponentially in the surface of porous media. By using Laplace and Fourier transform with the eigenvalues scheme, the physical quantities are analytically presented. The surface is shocked by thermal (pulse heat flux problems) and applying the traction free on its outer surfaces (mechanical boundary) through transport (diffusion) process of temperature to observe the analytical complete expression of the main physical fields. The change in volume fraction field, the variations of the displacement components, temperature and the components of stress are graphically presented. Suitable discussion and conclusions are presented.

• Coupled systems mechanics
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• 제11권3호
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• pp.199-215
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• 2022

The present paper deals with the axisymmetric deformation in homogeneousisotropic thermoelastic solid with two temperatures, with and without energy dissipation using modified couple stresstheory. The effect of energy dissipation and two temperature isstudied due to the concentrated normalforce, normalforce overthe circularregion, thermal pointsource and thermalsource over the circular region. The Laplace and Hankel transform techniques have been used to find the solution to the problem. The displacement components, conductive temperature distribution, stress components and couple stress are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. Effects of two temperature and energy dissipation on the conductive temperature,stress components and couple stress are depicted graphically.

• Structural Engineering and Mechanics
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• 제81권5호
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• pp.529-537
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• 2022

The present research is to study the effect of inclined load in a two-dimensional homogeneous orthotropic magneto-thermoelastic solid without energy dissipation with fractional order heat transfer in generalized thermoelasticity with two-temperature. We obtain the solution to the problem with the help of Laplace and Fourier transformations. The field equations of displacement components, stress components and conductive temperature are computed in transformed domain. Further the results are computed in physical domain by using numerical inversion method. The effect of fractional order parameter and inclined load has been depicted on the resulting quantities with the help of graphs.

• Coupled systems mechanics
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• 제11권5호
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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.

• 대한수학회보
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• 제60권2호
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• pp.361-388
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• 2023

In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.

• 호남수학학술지
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• 제45권4호
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• pp.619-628
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• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• Advances in nano research
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• 제16권6호
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• pp.549-564
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• 2024

This paper aims to analyze the dynamic response of thermoelectric carbon nanotube-reinforced composite (CNTRC) beams under moving harmonic load resting on Pasternak elastic foundation. The governing equations of thermoelectric CNTRC beam are obtained based on the Karama shear deformation beam theory. The beams are resting on the Pasternak foundation. Previous articles have not performed the moving load mode with the analytical method. The exact solution for the transverse and axial dynamic response is presented using the Laplace transform. A comparison of previous studies has been published, where a good agreement is observed. Finally, some examples were used to analyze, such as excitation frequency, voltage, temperature, spring constant factors, the volume fraction of Carbon nanotubes (CNTs), the velocity of a moving harmonic load, and their influence on axial and transverse dynamic and maximum deflections. The advantages of the proposed method compared to other numerical methods are zero reduction of the error percentage that exists in numerical methods.

• Structural Engineering and Mechanics
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• 제90권3호
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• pp.263-272
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• 2024

This research deals with the study of two-dimensional deformation in transversely isotropic thermoelastic diffusion medium. This investigation integrates the effect of diffusion and thermal effects in transversely isotropic thermoelastic solids under inclined load. Inclined load is taken as linear combination of normal load and tangential load. Laplace and Fourier transformation techniques are employed to transform the physical domain and then transformed solutions are inverted with the aid of numerical inversion techniques. Concentrated and distributed load are considered to exemplify its utility. Graphical representation of variation in displacement, stresses, temperature and concentration distribution with distance is depicted by taking inclination at different angles. Some particular cases are studied.