Passing through the elastic wave barrier by a load moving uniformly along a smoothly inhomogeneous elastic system

Abstract

The passing through the elastic wave barrier velocity is investigated for the case of a uniform load motion along a string on an elastic foundation. The string and foundation parameters vary 'smoothly' in such a manner that a transition from sub- into supercritical load motion occurs as the load passes a region of inhomogeneity. The transient solution for the string vibrations is derived and studied as a function of a characteristic length of the region of inhomogeneity. It turns out that during the passing the string displacements remain limited. It is shown that the smaller the characteristic length the smaller is the maximum amplitude of the string vibrations.