In-plane free vibration of supported/free parabolic cables

The free-vibration analysis of parabolic cables fixed at the lower end and free to move in the horizontal direction at the upper end is performed. The dynamic stiffness of such cables is zero at the natural frequencies and this property is used to obtain the governing frequency equation. Double-frequency points at which two consecutive natural frequencies are identical occur for specific values of stiffness parameters. Expressions for the natural modes of vibration and for the contribution of the extensional and inextensional cable resistances to the modal potential energy are given.