The coupled non-linear differential equations of cable vibration due to tra
nsverse and vertical multiple support excitations are formulated. The phase
difference between the input support excitations at cable ends is consider
ed 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 solutio
n. The stability of the steady state solution is examined. Numerical exampl
es are presented to compare the results with those of a finite element anal
ysis. The effects of cable sag and phase difference between the input suppo
rt excitations on the response are analyzed. The results show good agreemen
t between the analytical and numerical solutions especially near the resona
nce frequency. Considering phase differences between the support excitation
s at the cable ends is important because in this case the anti-symmetric mo
des are excited. (C) 2000 Elsevier Science Ltd. All rights reserved.