Analytical method for vibration with small amplitude superposed on static suspended configuration

The Eulerian description of the dynamic equations and analytical method for cables is given under the theoretical frame of dynamic problem, which superpose small deformation on the static suspended configuration of the cable. On condition that the small tensile flexibility and small amplitude vibration on static suspended configuration, the result present the out-plane vibration has no coupling with the in-plane vibration, and the in-plane vertical vibration and horizontal vibration can be decoupled. Comparing with the results obtained by using the ABAQUS code, the present method possesses higher precision and efficiency in which the relative error less than 4% and fluctuate fades rapidly, particularly for the small amplitude vibration with big sag.