On the lamb problem with long-range elastic cohesion forces

The Lamb two-dimensional problem involving a nonlocal medium is solved by taking the constitutive equations in the Kroener—Eringen form. The Fourier exponential transform procedure leads to the equations for stresses which are subject to time-dependent boundary conditions. In the particular case of a concentrated line force, the displacements at the surface of the half-space become associated with Rayleigh, longitudinal and shear waves whose velocities in the nonlocal case and for short waves are, by about 36%, less than those of their conventional counterparts.