ANALITICAL SOLUTIONS OF AN OSCILLATING ELASTIC CABLE LOADED WITH A CONCENTRATED MASS

We present a new analytical study of the oscillations of an elastic cable, loaded with a point mass in the center of the span. The solutions of the equations of motion represent a generalization of the linear theory of Irvine for the empty elastic cable, i.e. we find the transcendental equations to determine the eigenfrequencies for symmetric/antisymmetric modes of oscillations, as well as the eigenfunctions to determine the displacement of the cable. To test our analytical results we used a simple model of discrete mass points in the gravitational potential, connected by massless elastic rods.