Effect of bending stiffness and impact of key system parameters on the in-plane free vibration behavior of a two-cable network

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering 2024, Vol.46 (1), Article 43
• Main Authors: Ahmad, Javaid, Chaudhary, Muhammad Tariq A.
• Format: Article
• Language: English
• Subjects: Bending; Cable-stayed bridges; Cables; Cost analysis; Engineering; Finite element method; Free vibration; Mathematical models; Mechanical Engineering; Networks; Numerical models; Parameters; Partial differential equations; Physical properties; Resonant frequencies; Stiffness; Technical Paper
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-023-04593-0

Generally, cables in cable-stayed bridges are modeled and designed as taut strings. This assumption simplifies the analytical formulation in a cross-tied cable network, which offers a cost-effective solution for mitigation of cable vibrations. However, such a solution is strongly influenced by the physical properties of the main cables and the cross-tie. The modal parameters of stay cables are also known to be affected by their bending stiffness. This study presents an analytical formulation for determining the modal parameters of such cable networks in which cable bending stiffness is included. The resulting 4th-order partial differential equation for the flexible cable network was numerically solved, and the analytically obtained modal frequencies of the example cable networks were compared with the values obtained from FEM numerical model and an excellent match between the two sets of values was obtained. The deviation between modal frequencies of taut and flexible cable networks was found to have a maximum value of 10.7% and 3.08% for cables with high and average bending stiffness parameter ( μ ), respectively. However, the inclusion of bending stiffness had negligible influence on the mode shapes regardless of the μ value. After validation of the method, a parametric study was conducted that explored the impact of length ratio, frequency ratio, and bending stiffness ratio on the fundamental frequency of a flexible two-cable network. Bending stiffness ratio parameter of the main cables ( ξ ) played a significant role in increasing the fundamental frequency when the main cables had the same frequency ratio ( η = 1 ), while its effect diminished with decreasing value of η and the length ratio parameter ( ρ ) was more influential in  increasing  the fundamental frequency in such cases.