FLUID FLOW-INDUCED NONLINEAR VIBRATION OF SUSPENDED CABLES

The nonlinear interaction of the first two in-plane modes of a suspend ed cable with a moving fluid along the plane of the cable is studied. The governing equations of motion for two-mode interaction are derived on the basis of a general continuum model. The interaction causes the modal differential equations of the cable to be non-self-adjoint. As the flow speed increases above a certain critical value, the cable exp eriences oscillatory motion similar to the flutter of aeroelastic stru ctures. A co-ordinate transformation in terms of the transverse and st retching motions of the cable is introduced to reduce the two nonlinea rly coupled differential equations into a linear ordinary differential equation governing the stretching motion, and a strongly nonlinear di fferential equation for the transverse motion. For small values of the gravity-to-stiffness ratio the dynamics of the cable is examined usin g a two-time-scale approach. Numerical integration of the modal equati ons shows that the cable experiences stretching oscillations only when the flow speed exceeds a certain level. Above this level both stretch ing and transverse motions take place. The influences of system parame ters such as gravity-to-stiffness ratio and density ratio on the respo nse characteristics are also reported.