Stochastic thermal shock problem in generalized thermoelasticity

Sherief, Hany H.; El‐Maghraby, Nasser M.; Allam, Allam A.

doi:10.1016/j.apm.2012.02.056

Cited by 45 publications

(19 citation statements)

References 36 publications

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“…This theory was extended to deal with micropolar media [6], viscoelastic media [7], and poroelastic media [8]. It was also used to solve a problem with stochastic boundary conditions [9].…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional generalized thermoelastic diffusion problem for a half-space

El-Sayed

2016

Mathematics and Mechanics of Solids

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In this work, we consider the two-dimensional problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and subjected to a time-dependent thermal shock. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transforms. Numerical results are represented graphically and discussed.

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“…This theory was extended to deal with micropolar media [6], viscoelastic media [7], and poroelastic media [8]. It was also used to solve a problem with stochastic boundary conditions [9].…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional generalized thermoelastic diffusion problem for a half-space

El-Sayed

2016

Mathematics and Mechanics of Solids

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“…All these trajectories are considered as solutions for our stochastic model, but some trajectories may be more probable than others. Thus, instead of dealing with only one of these trajectories, we derive mathematically the mean and variance of the stochastic tsunami waveforms to get a better insight of the overall behavior of the stochastic tsunami waveforms; see [35]. First, we derive the mean of the tsunami waveforms by expressing the transformed free surface elevation, * * ( 1 , 2 , ), using (27) and (29)…”

Section: Mathematical Derivation Of the Mean And Variance Of The Stocmentioning

confidence: 99%

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Allam

Omar

Ramadan

2014

ISRN Applied Mathematics

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Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the x- and y-directions are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading uplift length and rise times of the three-dimensional stochastic fault source model. Tsunami waveforms within the frame of the linearized shallow-water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space). The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to the geometric spreading and also due to dispersion. The maximum amplitude amplification is proportional to the propagation length of the stochastic source model and inversely proportional to the water depth. The increase of the normalized noise intensities on the bottom topography leads to an increase in oscillations and amplitude in the free surface elevation. We derived and analyzed the mean and variance of the random tsunami waves as a function of the propagated uplift length, noise intensities, and the average depth of the ocean along the generation and propagation path.

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“…Val’kovskaya and Lenyuk [49] considered the problems involving stochastic internal heat generation. Sherief et al [50, 51] discussed the stochastic thermal shock problems in generalized thermoelasticity and generalized thermoelastic diffusion, respectively. Subsequently, Kant and Mukhopadhyay [52, 53] discussed the effects of the stochastic thermomechanical loading effects in the contexts of the theory of thermoelasticity without energy dissipation and the theory of thermoelasticity with two relaxation parameters.…”

Section: Introductionmentioning

confidence: 99%

Stochastic thermoelastic interaction under a dual phase-lag model due to random temperature distribution at the boundary of a half-space

Gupta

Mukhopadhyay

2018

Mathematics and Mechanics of Solids

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In the present work, we discuss the thermoelastic interactions in a half-space in the context of the theory of dual phase-lag thermoelasticity due to stochastic conditions applied at the boundary. We consider a one-dimensional problem with traction-free boundary subjected to two types of time-dependent thermal distributions. The boundary conditions are assumed to be random in nature to make the problem more realistic and the noise added is considered to be white noise. The problem is solved using Laplace transform and short time approximation is used to find the approximate solution for field variables while taking the inverse transforms. The solution for the stochastic case has been obtained by using the concept of a Wiener process and stochastic simulation. Numerical analysis based on stochastic simulation is carried out using copper material along different sample paths and comparative analysis between the deterministic and the stochastic distributions of field variables is presented. Special attention is paid to highlight the effects of considering randomness added to the boundary conditions.

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Stochastic thermal shock problem in generalized thermoelasticity

Cited by 45 publications

References 36 publications

A two-dimensional generalized thermoelastic diffusion problem for a half-space

A two-dimensional generalized thermoelastic diffusion problem for a half-space

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Stochastic thermoelastic interaction under a dual phase-lag model due to random temperature distribution at the boundary of a half-space

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