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Article

Stochastic Vibration of Damaged Cable System Under Random Loads

by
Yihao Wang
1,
Wei Li
1,* and
Drazan Kozak
2
1
School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
2
Mechanical Engineering Faculty, University of Slavonski Brod, Trg Ivane Brlic Mazuranic 2, HR-35000 Slavonski Brod, Croatia
*
Author to whom correspondence should be addressed.
Vibration 2025, 8(3), 44; https://doi.org/10.3390/vibration8030044
Submission received: 23 June 2025 / Revised: 26 July 2025 / Accepted: 2 August 2025 / Published: 4 August 2025

Abstract

This study proposes an integrated framework that combines nonlinear stochastic vibration analysis with reliability assessment to address the safety issues of cable systems under damage conditions. First of all, a mathematical model of the damaged cable is established by introducing damage parameters, and its static configuration is determined. Using the Pearl River Huangpu Bridge as a case study, the accuracy of the analytical solution for the cable’s sag displacement is validated through the finite difference method (FDM). Furthermore, a quantitative relationship between the damage parameters and structural response under stochastic excitation is developed, and the nonlinear stochastic dynamic equations governing the in-plane and out-of-plane motions of the damaged cable are derived. Subsequently, a Gaussian Radial Basis Function Neural Network (GRBFNN) method is employed to solve for the steady-state probability density function of the system response, enabling a detailed analysis of how various damage parameters affect structural behavior. Finally, the First-Order and Second-Order Reliability Method (FORM/SORM) are used to compute the reliability index and failure probability, which are further validated using Monte Carlo simulation (MCS). Results show that the severity parameter η shows the highest sensitivity in influencing the failure probability among the damage parameters. For the system of the Pearl River Huangpu bridge, an increase in the damage extent δ from 0.1 to 0.4 can reduce the reliability-based service life of by approximately 40% under fixed values of the damage severity and location, and failure risk is highest when the damage is located at the midspan of the cable. This study provides a theoretical framework from the point of stochastic vibration for evaluating the response and associated reliability of mechanical systems; the results can be applied in practice with guidance for the engineering design and avoid potential damages of suspended cables.
Keywords: suspended cables; nonlinear stochastic vibration; Gaussian radial basis function neural network; reliability function; failure probability suspended cables; nonlinear stochastic vibration; Gaussian radial basis function neural network; reliability function; failure probability

Share and Cite

MDPI and ACS Style

Wang, Y.; Li, W.; Kozak, D. Stochastic Vibration of Damaged Cable System Under Random Loads. Vibration 2025, 8, 44. https://doi.org/10.3390/vibration8030044

AMA Style

Wang Y, Li W, Kozak D. Stochastic Vibration of Damaged Cable System Under Random Loads. Vibration. 2025; 8(3):44. https://doi.org/10.3390/vibration8030044

Chicago/Turabian Style

Wang, Yihao, Wei Li, and Drazan Kozak. 2025. "Stochastic Vibration of Damaged Cable System Under Random Loads" Vibration 8, no. 3: 44. https://doi.org/10.3390/vibration8030044

APA Style

Wang, Y., Li, W., & Kozak, D. (2025). Stochastic Vibration of Damaged Cable System Under Random Loads. Vibration, 8(3), 44. https://doi.org/10.3390/vibration8030044

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