STRONG NONLINEAR MODAL INTERACTION IN SHALLOW SUSPENDED CABLES WITH OSCILLATING ENDS

This paper examines essentially nonlinear regimes of the stretching-be nding interactions in suspended cables with horizontally vibrating end s. Using a special nonlinear transformation of coordinates in the conf iguration space, the Lagrange function of the cable is written in term s of physical coordinates such as stretching and bending-swinging whic h possess different time scales. The transformed system is considered as a quasi-linear one with respect to the fast varying stretching gene ralized coordinate. The relatively slow bending-swinging component of the motion is described by strongly nonlinear equations on an 'unstret ched manifold'. It has been shown that the stretching natural frequenc y strongly depends on the bending position of the cable. As a result, the cable performs a chaos-like stretching-bending interaction around the resonance region, i.e. when the frequency of shaking is equal to t he natural frequency of stretching computed for an undeformed position of the cable. Outside the resonance region the motion has a regular c haracter. (C) 1997 Elsevier Science Ltd.