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

Abstract

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.

A novel stochastic photo-thermoelasticity model according to a diffusion interaction processes of excited semiconductor medium

“…Now, a stochastic distribution of the temperature (thermal) at the boundary can be defined on the following form [ 32 , 33 ]: where , is a constant temperature, is the Heaviside unit function, and a stochastic process is which is based on the time-parameter and satisfies: …”

“…6.1 , under the deterministic boundary condition Eqs. ( 24 ) and ( 21 ), the solution of the deterministic stress field can be described as [ 32 , 33 ]: …”

“…( 30 ) by the same technique which is used in Sect. 6.1 , the mean displacement distribution can be written as [ 32 , 33 ]: where the mean of all the displacement field sample paths has the similar solution of the deterministic case.…”

“…Allam et al [ 31 , 32 ] studied a stochastic half-space problem under the effect of an internal heat source in the theory of generalized diffusion—thermoelasticity theory in an infinitely long annular cylinder. Gupta and Mukhopadhyay [ 33 ] investigated the stochastic thermoelastic interaction with random temperature distribution at the free surface of an elastic solid medium under a dual phase-lag model. On the other hand, Kant and Mukhopadhyay [ 34 ] used the stochastic temperature distribution at the boundary to describe an elastic half-space problem.…”

A Novel Stochastic Model of the Photo-Thermoelasticity Theory of the Non-Local Excited Semiconductor Medium

“…Allam et al [25,26] studied a stochastic half-space problem under the effect of an internal heat source in the theory of generalized diffusion -thermoelasticity theory in an infinitely long annular cylinder. Gupta and Mukhopadhyay [27] investigated the stochastic thermoelastic interaction with random temperature distribution at the free surface of an elastic solid medium under a dual phase-lag model. On the other hand, Kant and Mukhopadhyay [28] used the stochastic temperature distribution at the boundary to describe an elastic half-space problem.…”