Eigenoscillations of an elastic cable
The eigenoscillations of a cable, supported at its end points, in a homogeneous gravitational field is investigated under the assumption that the bending stiffness is negligible but the behavior with respect to tension stresses is perfectly elastic. The problem involves two coupled second order equations and one independent second order equation; it is shown to be definitely self-adjoint and an iterative method for its solution is suggested. In the particular case of a shallow cable, that is with negligible sag, the asymptotic eigenvalues are obtained. It turns out that the gravitational field has such a "stiffening" effect that the eigenvalues related to some oscillation modes may be substantially greater (the lowest of them eightfold) than those given in the classical theory on vibrating strings.