On the oscillatory motions of translating elastic cables

Some approximations for the dynamics of spacecraft tethers

“…(17) into Eqs. (15) and (16) yields a pair of coupled second order polynomials in y and co. These polynomials are satisfied along the lines sketched in Fig.…”

“…The curve need not be shallow, nor need the radius of curvature R be constant with s. It is clear that curvature couples the two components of the planar motions; Eqs. (15) and (16) are coupled by terms involving l/R. As R-*co 9 the coupling disappears, and the equations are reduced to the familiar decoupleH wave equations for axial and lateral motion of an elastic cable.…”

Dynamics of Mooring Cables in Random Seas

“…By considering an in"nitesimal cable element, we can de"ne the equations governing the total dynamic displacements u R (s, t) and v R (s, t) along the directions of the x-and y-axis, respectively, following Simpson (1972) and Hagedorn & SchaK fer (1980). The mooring cable is assumed to have the following parameters: m is the mass per unit length of the cable (including added mass); U is the density of water; d is the diameter of the cable;…”

Nonlinear free vibrations of coupled spans of overhead transmission lines

“…In the second type elasticity is only important in the higher orders, and to leading order the tension vanishes. The probably best studied cable motion is the symmetric mode with fixed ends (a single span mode) which is an example of an elasto-gravity mode [3,5,7,8,[13][14][15][16][17]. Higher order, asymmetric modes of singles spans may be of gravity-mode type.…”