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.