In the absence of sag, the mode shapes of a cable with fixed ends are simple sine functions. However, with sag, the mode shapes that are symmetric about the center of the cable change. The antisymmetric ones do not.
This is an animation to show how these mode shapes change with increasing levels of sag. Actually, the effects of sag, inclination, and axial flexibility can all be captured with one independent parameter, l2 (lambda^2). The animation starts with l2 = 0 and increases to 500. Stay cables on cable-stayed bridges have l2 on the order of 1. Transmission lines typically are around 90, and suspension bridge main cables in the 140-350 range.
The animation may be viewed in one of several formats:E.A. Johnson, R.E. Christenson, and B.F. Spencer, Jr., "Semiactive Damping of Cables with Sag," Computer Aided Civil and Infrastructure Engineering, submitted.Cable dynamics in general are discussed extensively in this classic text:
H.M. Irvine, Cable Structures, MIT Press, Cambridge, Massachusetts, 1981.If you have any questions or comments, please let me know.
