On the oscillatory motions of translating elastic cables

The equations of in-plane motion for an elastic catenary translating uniformly between its end supports are derived in what is, essentially, an Eulerian frame of reference. These equations are solved analytically, albeit approximately, for the case where the catenary is shallow and the tension dominated by the cable section modulus. Computed solutions for the natural frequencies and modes of a catenary of sag-span ratio 1:20 are presented and the modal characteristics are shown to be of an unusual form involving phase disparities from point to point on the cable as the cable oscillates at a natural frequency.