Influence of the Tension Variety on Non-Linear Natural Frequency of an Inclined Cable

According to the vibration characteristics of small sag cable, an equation of non-linear free transverse in-plane vibration of an inclined cable is presented considering the effects of the flexural rigidity. In the equation the influence of the tension variety along the inclined cable was taken into account by using the precise parabola equation of the taut cable. Taking single mode of a cable in consideration, the governing equation was simplified as a traditional Duffing equation with a quadratic term. It was solved by using the method of Fourier series. Combined with engineering practice, an example was provided to study nonlinear natural vibration characteristic of an inclined cable in plane when the length, the inclination angle, the tension were changed separately, whether considering the influence of tension variety along the inclined cable or not.