International Journal of Non-Linear Mechanics 40 (2005) 571 – 588 www.elsevier.com/locate/nlm One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models Vincenzo Gattulli a , ∗ , Marco Lepidi b , John H.G. Macdonald c , Colin A. Taylor c a Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, Università di L’Aquila, Monteluco di Roio, Italy b Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, Roma, Italy c Department of Civil Engineering, University of Bristol, Bristol, UK Received 3 March 2004; received in revised form 27 August 2004; accepted 27 August 2004 Abstract The mechanism of cable end angle-variation induced oscillations in the non-linear interactions between beams and cables in stayed-systems is first explained by a proposed analytical model. It is then verified by both experimental and finite element models. The non-linear interaction maximizes its effects for cable oscillations when inherent quadratic coupling between local and global modes produces energy transfer from low to high frequency vibrations by means of a one-to-two global–local autoparametric resonance. The response of the analytical model is fully described using a continuation method applied directly to the reduced two degree of freedom discrete model showing that, for a selected one-to-two global–local resonant system, primary harmonic excitation of the global mode produces large oscillations of the local mode at twice the excitation frequency. Detailed comparisons between the responses of the analytical model, experimental results and finite element simulations show excellent agreement both in the qualitative behaviour and in the calculated/measured response amplitudes.  2004 Elsevier Ltd. All rights reserved. Keywords: Cables; Cable-stayed beam; Experimental methods; Dynamic interaction; Non-linear oscillations; Energy transfer; Autoparametric resonance; Finite element method 1. Introduction During the past decade cable-supported structures, in a variety of geometric configurations, have found ∗ Corresponding author. Tel.: +39 0862 434511; fax: +39 0862 434548. E-mail address: gattulli@ing.univaq.it (V. Gattulli). 0020-7462/$ - see front matter  2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijnonlinmec.2004.08.005 wide application throughout the world for stayed bridges, guyed towers and suspended roofs. Due to their lightness, flexibility and inherently low damping characteristics [1], stayed structures are susceptible to significant vibrations. Also, the natural frequen- cies of overall structural motions are often close to those of individual cables. This situation can lead to cable–structure interaction mechanisms which