Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks Gian Felice Giaccu a,b,1 , Luca Caracoglia b,n a Dipartimento di Ingegneria Civile, Ambientale e Architettura, Universit  a di Cagliari, 09123 Cagliari, Italy b Department of Civil and Environmental Engineering, Northeastern University, Boston, MA 02115, USA article info Article history: Received 3 May 2012 Received in revised form 30 November 2012 Accepted 7 December 2012 Handling Editor: W. Lacarbonara abstract Cross-ties are used for mitigating stay-cable vibration, induced by wind and wind-rain on cable-stayed bridges. In-plane cable networks are obtained by connecting the stays by transverse cross-ties. While taut-cable theory has been traditionally employed for simulating the dynamics of cable networks, the use of a nonlinear restoring-force discrete element in each cross-tie has been recently proposed to more realistically replicate the network vibration when snapping or slackening of the restrainer may be anticipated. The solution to the free-vibration dynamics can be determined by ‘‘equiva- lent linearization method’’. In an exploratory study by the authors a cubic-stiffness spring element, in parallel with a linear one, was used to analyze the restoring-force effect in a cross-tie on the nonlinear dynamics of two simplified systems. This preliminary investigation is general- ized in this paper by considering a power-law stiffness model with a generic integer exponent and applied to a prototype network installed on an existing bridge. The study is restricted to the fundamental mode and some of the higher ones. A time-domain lumped-mass algorithm is used for validating the equivalent linearization method. For the prototype network with quadratic-stiffness spring and a positive stiffness coefficient, a stiffening effect is observed, with a ten percent increment in the equivalent frequency for the fundamental mode. Results also show dependency on vibration amplitude. For higher modes the equivalent nonlinear effects can be responsible for an alteration of the linear mode shapes and a transition from a ‘‘localized mode’’ to a ‘‘global mode’’. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction With the progressive increase in the spans of cable-stayed bridges in the last decades, inclined stays may reach unprecedented lengths of several hundred meters and become extremely susceptible to wind loading. Cross-ties are employed as passive devices for the mitigation of stay cable vibration, which have been observed under the excitation of wind and wind–rain (e.g., [1,2]). Several models exist for predicting the loading mechanisms and stay vibration. As an example, the ‘‘dry galloping’’ mechanism has been used for the interpretation of the large-amplitude oscillation (e.g., [3,4]). Excitation and primary vibration in the stays have been clearly observed in a full scale investigation (e.g., [5]). Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration 0022-460X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jsv.2012.12.006 n Correspondence to: Department of Civil and Environmental Engineering, Northeastern University, 400 Snell Engineering Center, 360 Huntington Avenue, Boston, MA 02115, USA. Tel.: þ1 617 373 5186; fax: þ1 617 373 4419. E-mail address: lucac@coe.neu.edu (L. Caracoglia). 1 Post-doctoral Fellow at Northeastern University, February 2012 to October 2012. Journal of Sound and Vibration ] (]]]]) ]]]–]]] Please cite this article as: G.F. Giaccu, & L. Caracoglia, Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks, Journal of Sound and Vibration (2013), http://dx.doi.org/10.1016/j.jsv.2012.12.006i