On the Wave Propagation in an Elastic Hollow Cylinder With Long-Range Cohesion Forces

Abstract

After a brief derivation of the formula for the nonlocal moduli, Fourier transforms of the stress components in their nonlocal aspect are established. Satisfaction of the traction-free boundary conditions leads to the frequency equation of the problem. A particular case involving longitudinal Lamé modes is analyzed in more detail. A numerical example solved shows a considerable decrease of the speed and the frequency of the short waves as compared with those of long waves studied in the classical theory.