In-Plane Free Vibrations of an Inclined Taut Cable

The investigation of the free vibrations of inclined taut cables has been a significant subject due to their wide applications in various engineering fields. For this subject, accurate analytical expression for the natural modes and the natural frequencies is of great importance. In this paper, the free vibration of an inclined taut cable is further investigated by accounting for the factor of the weight component parallel to the cable chord. Two coupled linear differential equations describing two-dimensional in-plane motion of the cable are derived based on Newton’s law. By variable substitution, the equation of the transverse motion becomes a Bessel equation of zero order when the equation of longitudinal motion is ignored. Solving the Bessel equation with the given boundary conditions, a set of explicit formulae is presented, which is more accurate for determining the natural frequencies and the modal shapes of an inclined taut cable. The accuracy of the proposed formulae is validated by numerical results obtained by the Galerkin method. The influences of two characteristic parameters $λ$ and $ε$ on the natural frequencies and modal shapes of an inclined taut cable are studied. The results are discussed and compared with those of other literatures. It appears that the present theory has an advantage over others in the aspect of accuracy, and may be used as a base for the correct analysis of linear and nonlinear dynamics of cable structures.