{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:27:07Z","timestamp":1760149627337,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Sciences and Engineering Research Council of Canada (NSERC)","award":["RGPIN-2022-02973"],"award-info":[{"award-number":["RGPIN-2022-02973"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Cross-ties have proven their efficacy in mitigating vibrations in bridge stay cables. Several factors, such as cross-tie malfunctions due to slackening or snapping, as well as the utilization of high-energy dissipative materials, can introduce nonlinear restoring forces in the cross-ties. While previous studies have investigated the influence of the former on cable network dynamics, the evaluation of the impact of nonlinear cross-tie materials remains unexplored. In this current research, an existing analytical model of a two-shallow-flexible-cable network has been extended to incorporate the cross-tie material nonlinearity in the formulation. The harmonic balance method (HBM) is employed to determine the equivalent linear stiffness of the cross-ties. The dynamic response of a cable network containing nonlinear cross-ties is approximated by comparing it to an equivalent linear system. Additionally, the study delves into the effects of the cable vibration amplitude, cross-tie material properties, installation location, and the length ratio between constituent cables on both the fundamental frequency of the cable network and the equivalent linear stiffness of the cross-ties. The findings reveal that the presence of cross-tie nonlinearity significantly influences the in-plane modal response of the cable network. Not only the frequencies of all the modes are reduced, but the formation of local modes is delayed to a high order. In contrast to an earlier finding based on a linear cross-tie assumption, with nonlinearity present, moving a cross-tie towards the mid-span of a cable would not enhance the in-plane stiffness of the network. Moreover, the impact of the length ratio on the network in-plane stiffness and frequency is contingent on its combined effect on the cross-tie axial stiffness and the lateral stiffness of neighboring cables.<\/jats:p>","DOI":"10.3390\/computation11090169","type":"journal-article","created":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T08:19:39Z","timestamp":1693556379000},"page":"169","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Impact of Cross-Tie Material Nonlinearity on the Dynamic Behavior of Shallow Flexible Cable Networks"],"prefix":"10.3390","volume":"11","author":[{"given":"Amir","family":"Younespour","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, Canada"}]},{"given":"Shaohong","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1016\/S0141-0296(98)00028-5","article-title":"Recent evolution of cable-stayed bridges","volume":"21","author":"Virlogeux","year":"1999","journal-title":"Eng. 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