# In-Plane Vibration Analysis of a Multi-Cable-Stayed Beam Carrying Concentrated Masses and the Impact of Thermal Effects

 International Journal of Civil Engineering © 2024 by SSRG - IJCE Journal Volume 11 Issue 6 Year of Publication : 2024 Authors : Mohamed Rjilatte, Ahmed Adri, Omar Outassafte, Issam El Hantati, Yassine El Khouddar, Mohamed Berjal, Rhali Benamar 10.14445/23488352/IJCE-V11I6P112
##### How to Cite?

Mohamed Rjilatte, Ahmed Adri, Omar Outassafte, Issam El Hantati, Yassine El Khouddar, Mohamed Berjal, Rhali Benamar, "In-Plane Vibration Analysis of a Multi-Cable-Stayed Beam Carrying Concentrated Masses and the Impact of Thermal Effects," SSRG International Journal of Civil Engineering, vol. 11,  no. 6, pp. 107-119, 2024. Crossref, https://doi.org/10.14445/23488352/IJCE-V11I6P112

##### Abstract:

In this paper, we proposed a linear model to analyze the transverse vibrations in the plane of a beam suspended by cables. We conducted a dynamic study of this structure, and the results of the frequencies, as well as the mode shapes of the beam, were obtained. We began our methodology by introducing the equations of motion, which were established at various intervals in the plane of the system, along with their boundary and continuity conditions. Subsequently, we iteratively solved the generalized transcendental frequency equation using the Newton-Raphson method. Once our results were validated by existing literature, we continued our analysis by conducting a parametric study. Masses at different positions and with different values were added, along with a thermal load. We obtained the numerical results of the dynamic study for different positions of the added masses and different values of the thermal load. Through this method, we were able to gain a thorough understanding of the dynamic behavior of the structure in different situations.

##### Keywords:

Cable-stayed beam, Linear frequencies.

##### References:

[1] Yunyue Cong et al., “Modeling, Dynamics, and Parametric Studies of a Multi-Cable-Stayed Beam Model,” Acta Mechanica, vol. 231, pp. 4947–4970, 2020.
[2] Y. Fujino, P. Warnitchai, and B.M. Pacheco, “An Experimental and Analytical Study of Autoparametric Resonance in a 3DOF Model of Cable-Stayed-Beam,” Nonlinear Dynamics, vol. 4, pp. 111–138, 1993.
[3] P. Warnitchai, Y. Fujino, and T. Susumpow, “A Non-Linear Dynamic Model for Cables and Its Application to a Cable-Structure System,” Journal of Sound and Vibration, vol. 187, no. 4, pp. 695–712, 1995.
[4] Yong Xia, and Yozo Fujino, “Auto-Parametric Vibration of a Cable-Stayed-Beam Structure under Random Excitation,” Journal of Engineering Mechanics, vol.132, no. 3, 2006.
[5] Xiaoyang Su et al., “Dynamic Analysis of the in-Plane Free Vibration of a Multi-Cable-Stayed Beam with Transfer Matrix Method,” Archive of Applied Mechanics, vol. 89, pp. 2431–2448, 2019.
[6] Hui Li et al., “Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers,” Journal of Bridge Engineering, vol. 12, no. 4, pp. 401–409, 2007 .
[7] M.H. El Ouni, N. Ben Kahla, and A. Preumont, “Numerical and Experimental Dynamic Analysis and Control of a Cable Stayed Bridge under Parametric Excitation,” Engineering Structures, vol. 45, pp. 244–256, 2012.
[8] Rujin Ma, Xinzhong Chen, and Airong Chen, “Effect of Cable Vibration on Aerostatic Response and Dynamics of a Long Span CableStayed Bridge,” New Horizons and Better Practices, pp. 1–10, 2012.
[9] Vincenzo Gattulli et al., “One-to-two Global-Local Interaction in a Cable-Stayed Beam Observed Through Analytical, Finite Element and Experimental Models,” International Journal of Non-Linear Mechanics, vol. 40, no. 4, pp. 571–588, 2005.
[10] Vincenzo Gattulli, Marco Lepidi, and A. Paolone, “A Parametric Analytical Model For Non-Linear Dynamics in Cable-Stayed Beam,” Earthquake Engineering & Structural Dynamics, vol. 31, no. 6, pp. 1281–1300, 2002.
[11] Vincenzo Gattulli, and Marco Lepidi, “Localization and Veering in the Dynamics of Cable-Stayed Bridges,” Computers & Structures,
vol. 85, no. 21–22, pp. 1661–1678, 2007.
[12] Vincenzo Gattulli, and Marco Lepidi, “Nonlinear Interactions in the Planar Dynamics of Cable-Stayed Beam,” International Journal of Solids and Structures, vol. 40, no. 18, pp. 4729–4748, 2003.
[13] Christos Aloupis, Michael J. Chajes, and Harry W. Shenton III, “Damage Identification in Cable-Stayed Bridges based on the Redistribution of Dead and Thermal Loads,” Engineering Structures, vol. 284, 2023.
[14] Wen-Ming Zhang et al., “Analytical Study on Free Vertical and Torsional Vibrations of Two- and Three-Pylon Suspension Bridges via D,” Structural Engineering and Mechanics, vol. 76, no. 3, pp. 293-310, 2020.
[15] A. Cunha, E. Caetano, and R. Delgado, “Dynamic Tests on Large Cable-Stayed Bridge,” Journal of Bridge Engineering, vol. 6, no. 1, pp. 54–62, 2001.
[16] Wei-XinRen, Xue-Lin Peng, and You-Qin Lin, “Experimental and Analytical Studies on Dynamic Characteristics of a Large Span Cable-Stayed Bridge,” Engineering Structures, vol. 27, no. 4, pp. 535–548, 2005.
[17] Ahmed M. Abdel-Ghaffar, and Magdi A. Khalifa, “Importance of Cable Vibration in Dynamics of Cable-Stayed Bridges,” Journal of Engineering Mechanics, vol. 117, no. 11, pp. 2571–2589, 1991.
[18] Aly S. Nazmy, and Ahmed M. Abdel-Ghaffar, “Effects of Ground Motion Spatial Variability on the Response of Cable-Stayed Bridges,” Earthquake Engineering & Structural Dynamics, vol. 21, no. 1, pp. 1–20, 1992.