Non-linear cable response to multiple support periodic excitation

The coupled non-linear differential equations of cable vibration due to transverse and vertical multiple support excitations are formulated. The phase difference between the input support excitations at cable ends is considered in the formulation of the equations of motion. Damping is not considered in this analysis. The spatial problem is solved by Galerkin method using a two degree of freedom model for the cable. The temporal problem is solved using the method of multiple time scales to obtain the steady state solution. The stability of the steady state solution is examined. Numerical examples are presented to compare the results with those of a finite element analysis. The effects of cable sag and phase difference between the input support excitations on the response are analyzed. The results show good agreement between the analytical and numerical solutions especially near the resonance frequency. Considering phase differences between the support excitations at the cable ends is important because in this case the anti-symmetric modes are excited.