THE STRUCTURE OF THE SOLUTION SET FOR PERIODIC OSCILLATIONS IN A SUSPENSION BRIDGE MODEL

Numerical results are reported for the computation of periodic solution paths for a suspension bridge model represented by the equation u(tt) + EIu(xxxx) + delta-u(t) + Ku+ = W(x) + lambda-sin pi-x sin-mu-t, with hinged-end boundary conditions, as the forcing amplitude-lambda and frequency-mu are varied. The term Ku+ models the fact that there is restoring force due to the cables only when they are being stretched. It is found that an S-shaped curve is obtained when the displacement amplitudes are plotted against the forcing amplitudes-lambda for some frequency regimes. As a two-parameter problem, it appears that the solution set resembles a cusp-like surface with the singular point near linear resonance. While the effect of strengthening the cable (i.e. increasing K) will enhance the occurrence of the multiple solutions, the effect of the damping coefficient gives the opposite effect.