On the torsional waves in an elastic bar with long-range cohesive forces

Abstract

With reference to some of the results obtained in [1], the equation of motion and the equations of nonlocal stress components in the form of Kroener-Eringen are transformed into the Fourier space. A lengthy calculation using a separable form of the nonlocal elastic moduli leads to the governing equation of the problem with two types of solutions. In each case the nonlocal phase velocity and, respectively, the nonlocal group velocity of the very short waves turn out to be by about 36% less than the velocities of their classical counterparts.