Effect of the Number of Cross-Tie Lines on the In-Plane Stiffness and Modal Behavior Classification of Orthogonal Cable Networks with Multiple Lines of Transverse Flexible Cross-Ties

Using cross-ties to connect a vulnerable cable with its neighbor(s) and forming a cable network is a common countermeasure to suppress bridge stay cable vibrations. An effective design of cross-tie solution should provide an optimum combination of cross-tie installation location, stiffness, and number of cross-tie lines to maximize the network in-plane frequency and structural damping while minimizing the number of excited local modes. However, the mechanics associated with cable networks is not as simple as their geometrical appearance. In particular, the addition of an extra line of cross-ties to an existing cable network would considerably increase the complexity of its structural behavior. While the effects of cross-tie position and stiffness on network response have been investigated in some existing studies, that associated with the number of cross-tie lines is scarce. For better understanding of how the dynamic behavior of a group of cables would be influenced when interconnected by different number of cross-tie lines, the current study proposes an analytical model of cable networks consisting of two parallel main cables interconnected by multiple lines of flexible transverse cross-ties. A new parameter, the degree of mode localization (DML), is introduced to quantitatively evaluate the global nature of a network mode. The in-plane modal responses of two cables when interconnected respectively by one, two, and three lines of cross-ties are analyzed and compared. A parametric study is conducted to assess the impact of various system properties on the in-plane frequency and local mode excitation of networks containing different number of cross-tie lines.