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.

Many mechanical systems manifest nonlinear behavior under nonstationary random excitations. Neglecting this nonlinearity in the modeling of a dynamic system would result in unacceptable results. However, it is challenging to find exact solutions to nonlinear problems. Therefore, equivalent linearization methods are often used to seek approximate solutions for this kind of problem. To overcome the limitations of the existing equivalent linearization methods, an orthogonal-function-based equivalent linearization method in the time domain is proposed for nonlinear systems subjected to nonstationary random excitations. The proposed method is first applied to a single-degree-of-freedom (SDOF) Duffing–Van der Pol oscillator subjected to stationary and nonstationary excitations to validate its accuracy. Then, its applicability to nonlinear MDOF systems is depicted by a 5DOF Duffing–Van der Pol system subjected to nonstationary excitation, with different levels of system nonlinearity strength considered in the analysis. Results show that the proposed method has the merit of predicting the nonlinear system response with high accuracy and computation efficiency. In addition, it is applicable to any general type of nonstationary random excitation.