One-dimensional wave propagation problem in a nonlocal finite medium with finite difference method

Abstract

In this work, the wave propagation problem in one - dimensional finite medium is investigated in the context of nonlocal continuum mechanics. The main purpose of the paper is to demonstrate the end effects. Numerical solutions are obtained by the finite difference method. Furthermore, the differences between the nonlocal infinite and nonlocal finite cases are shown. It is observed that the velocity of the propagating waves is slowing down and the amplitude is decreasing due to the end effects.