NORMAL-FORM TRANSFORMATION AND AN APPLICATION TO A FLUTTER-TYPE OF VIBRATION

Wake-induced oscillations affect bundled conductors of overhead transm ission lines exposed to moderate to strong crosswinds. They represent a flutter-type of vibration that arises from the shielding effects of windward conductors on leeward ones. We consider a twin horizontal bun dle of overhead lines. A mechanical model of this bundle is described by two cylinders mounted on springs, one in the wake of its neighbour. The critical wind velocity (bifurcation point) of incipient flutter i s identified (Kern and Maitz, 1994, Proc. VII Int. Conf. on Boundary a nd Int. Layers Comp. and Asymptotic Methods, Beijing, China; Kern et a l., 1995, SFB-Report 23, Institute of Mathematics, Graz). This bifurca tion point yields a generalized Hopf bifurcation with non-semisimple d ouble imaginary eigenvalues (case of 1:1 resonance). A non-linear anal ysis is adopted to investigate the post-bifurcational behaviour of the oscillations. In order to reduce the non-linear dynamical system to a simpler system without loss of generality of the dynamical behaviour, we use the normal form methods. In this method all non-linear terms w hich do not contribute to the dynamical behaviour are eliminated. Usin g a normal form transformation we get a three-dimensional system of am plitude equations which is analyzed qualitatively with regard to the u nfolding parameters. (C) 1998 Elsevier Science Ltd. All rights reserve d.