On the Wave Propagation in Non-Local Thermoelasticity with Time Delay

In this study, we proposed a new constitutive equation for spatially one-dimensional non-local elasticity in the presence of a non-uniform temperature distribution. The novelty consists in introduction of a new kernel and position dependent time delay. The kernel function of the general fractional derivative is of the Riesz-type. To address the simplification introduced by assuming an infinite speed of propagation-whereby strain instantaneously influences stress at a distant point — a time position dependent delay is introduced. Additionally, it is assumed that the temperature of the one-dimensional continuum is non-uniform and is prescribed in advance. The corresponding wave equation is derived for the described case. This generalized wave equation is then solved using Laplace and Fourier transforms. The influence of various problem parameters is investigated numerically. The extension of the previously established isothermal framework to non-isothermal problems represents a significant generalization and broadens the potential applications of the method.