PSI - Issue 83

Mohamed Berjal et al. / Procedia Structural Integrity 83 (2026) 295–304

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4. Conclusion In this work, the nonlinear vibration behavior of cable-stayed beams is investigated with a focus on elastic support parameters and material properties. The proposed formulation accurately captures both linear and nonlinear responses. The results show that increasing the cable Young’s modulus enhances the global stiffness, while higher rotational stiffness reduces sensitivity to cable effects. The nonlinear analysis reveals a hardening behavior, more pronounced for flexible supports and reduced in stiffer configurations. Curvature distributions highlight the limitations of linear models, especially under asymmetric boundary conditions. From an optimization perspective, tuning elastic support parameters, particularly rotational stiffness, allows effective control of the nonlinear response and improves vibration performance. These findings highlight that the appropriate tuning of elastic support parameters provides an effective strategy for optimization and control of nonlinear vibrations. Future work will consider damping, material nonlinearities, and more complex configurations. Acknowledgements The authors gratefully acknowledge the support of the Higher School of Technology of Casablanca, the National Higher School of Electricity and Mechanics of Casablanca, and Hassan II University of Casablanca. References A Semi-Analytical Approach to the Non-Linear Dynamic Response Problem of S-S and C-C Beams at Large Vibration Amplitudes Part I: General Theory and Application to the Single Mode Approach to Free and Forced Vibration Analysis, n.d. Bennouna, M.M., White, R.G., 1984. The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam. Journal of Sound and Vibration 96, 309–331. https://doi.org/10.1016/0022-460X(84)90359-6 Berjal, M., Adri, A., Hantati, I.E., Outassafte, O., Khouddar, Y.E., Rjilatte, M., Benamar, R., 2026. Single-Mode analytical modeling of geometrically nonlinear free vibrations in cable-stayed beams with elastic supports. Presented at the TECHNOLOGIES AND MATERIALS FOR RENEWABLE ENERGY, ENVIRONMENT AND SUSTAINABILITY: TMREES25Fr, Metz, France, p. 380001. https://doi.org/10.1063/12.0042874 Berjal, M., Adri, A., Outassafte, O., Hantati, I.E., Khouddar, Y.E., Rjilatte, M., Benamar, R., 2024a. Parametric Analysis Studies of the Vibrations of a Multi-Cable-Stayed Beam Resting on Elastic Suppor. SSRG-IJCE 11, 1–19. https://doi.org/10.14445/23488352/IJCE V11I7P101 Berjal, M., Adri, A., Outassafte, O., Hantati, I.E., Khouddar, Y.E., Rjilatte, M., Benamar, R., 2024b. Linear vibration analysis of multi-cable stayed beams resting on multiple elastic supports. Presented at the TRANSPORT, ECOLOGY - SUSTAINABLE DEVELOPMENT EKO VARNA 2024, Varna, Bulgaria, p. 020012. https://doi.org/10.1063/5.0247339 Cong, Y., Kang, H., Yan, G., Guo, T., 2020. Modeling, dynamics, and parametric studies of a multi-cable-stayed beam model. Acta Mech 231, 4947–4970. https://doi.org/10.1007/s00707-020-02802-8 El Bikri, K., Benamar, R., Bennouna, M., 2003. Geometrically non-linear free vibrations of clamped simply supported rectangular plates. Part I: the effects of large vibration amplitudes on the fundamental mode shape. Computers & Structures 81, 2029–2043. https://doi.org/10.1016/S0045-7949(03)00152-4 El Hantati, I., Outassafte, O., El Khouddar, Y., Belhaou, M., Adri, A., Benamar, R., 2024. Analysis of the transverse vibration of a multistepped FGM beam resting on a Winkler foundation in a thermal environment and carrying concentrated masses. Results in Engineering 23, 102822. https://doi.org/10.1016/j.rineng.2024.102822 El Kadiri, M., Benamar, R., White, R.G., 2002. IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED–CLAMPED AND SIMPLY SUPPORTED–CLAMPED BEAMS. Journal of Sound and Vibration 249, 263–305. https://doi.org/10.1006/jsvi.2001.3808 El Khouddar, Y., Adri, A., Outassafte, O., El Hantati, I., Rifai, S., Benamar, R., 2022. Influence of hygro-thermal effects on the geometrically nonlinear free and forced vibrations of piezoelectric functional gradient beams with arbitrary number of concentrated masses. Arch Appl Mech 92, 2767–2784. https://doi.org/10.1007/s00419-022-02219-w Kang, H., Cai, Y., Cong, Y., Su, X., Yan, G., 2022. Revealing energy transfer between deck and cables in cable-stayed bridges through resonancne analysis with coupling effect of adjacent cables considered. https://doi.org/10.21203/rs.3.rs-1403965/v1 Moussaoui, F., Benamar, R., White, R.G., 2000. THE EFFECTS OF LARGE VIBRATION AMPLITUDES ON THE MODE SHAPES AND NATURAL FREQUENCIES OF THIN ELASTIC SHELLS, PART I: COUPLED TRANSVERSE-CIRCUMFERENTIAL MODE SHAPES OF ISOTROPIC CIRCULAR CYLINDRICAL SHELLS OF INFINITE LENGTH. Journal of Sound and Vibration 232, 917–943. https://doi.org/10.1006/jsvi.1999.2770 Outassafte, O., Adri, A., Khouddar, Y.E., Hantati, I.E., Rifai, S., Benamar, R., 2024. Crack identification in circular arches through natural