Modal interactions around a multiple frequency veering in cable-stayed structures

The coupled dynamics of the deck and the stays in cable-stayed bridges offers a paradigmatic example of the rich scenario of modal interactions which characterizes the linear response of complex structures made of dissimilar component sub-systems. Their high spectral density favours the occurrence of multiple internal resonance between the global modes of the structure and the local modes of the sub-systems. This condition may lead to frequency veering and localization or hybridization of the modal shapes, enabling also the possibility of significant energy flows between the resonant modes. Although similar phenomena are commonly studied in periodic structures, since they arise when a band spectrum of many local frequencies is disturbed by a regularity-breaking perturbation, the modal interactions which is instead realized between global and local modes may present specific features. The sectional model presented in the paper is used to highlight the role played by different internal resonance conditions in the description of the cable-deck interactions. Resonant systems are investigated with focus on the sensitivity of the frequencies with respect to the significant parameters, and on the parameter-depending level of mode localization, evaluated by means of an energy-based factor. The veering phenomenon and the modal hybridization characterizing the 1:1 resonance between two local modes are initially described. Then attention is paid to the 1:1:1 resonance which might arise if a third frequency, of global type, is tuned with the local ones. The conditions which allow the occurrence of this multiple resonance are discussed, and the effects induced by the resonant global mode on the veering phenomenon and the hybridization process are described