PSI - Issue 83

Mohamed Rjilatte et al. / Procedia Structural Integrity 83 (2026) 208–217

216

Fig. 4: Curvatures of a cable-stayed beam clamped at both ends, near the first mode, for varying values of the maximum vibration amplitude .

4. CONCLUSION This study focused on the analysis of geometrically nonlinear vibrations of a beam suspended by cables. After solving the differential equation governing the vibratory behavior of the system, boundary and continuity conditions were applied to determine the linear frequencies and displacements, which serve as basic functions for the nonlinear analysis. Hamilton’s principle was then employed to express the system’s kinetic and potential energies, enabling the formulation of the system to be solved. The nonlinear behavior of the system was investigated using the single-mode approach. References [1] Y. Cong, H. Kang, G. Yan, et T. Guo, « Modeling, dynamics, and parametric studies of a multi-cable-stayed beam model », Acta Mech , vol. 231, n o 12, p. 4947 ‑ 4970, déc. 2020, doi: 10.1007/s00707-020-02802-8. [2] T. Guo, H. Kang, L. Wang, et Y. Zhao, « Nonlinear vibrations for double inclined cables–deck beam coupled system using asymptotic reductions », International Journal of Non-Linear Mechanics , vol. 108, p. 33 ‑ 45, janv. 2019, doi: 10.1016/j.ijnonlinmec.2018.10.003. [3] D.-X. Cao, Y.-W. Zhou, et X.-Y. Guo, « In-plane free vibration analysis of multi-folded beam structures », Engineering Structures , vol. 302, p. 117437, mars 2024, doi: 10.1016/j.engstruct.2023.117437. [4] R. Ma, X. Chen, et A. Chen, « Effect of Cable Vibration on Aerostatic Response and Dynamics of a Long Span Cable-Stayed Bridge », p. 1 ‑ 10, juin 2012, doi: 10.1061/40946(248)80. [5] X. Su, H. Kang, T. Guo, et Y. Cong, « Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper », Nonlinear Dyn , vol. 110, n o 1, p. 131 ‑ 152, sept. 2022, doi: 10.1007/s11071-022-07644-8. [6] M. El Kadiri et R. Benamar, « Improvement of the semi-analytical method, based on Hamilton’s principle and spectral analysis, for determination of the geometrically non-linear response of thin straight structures. Part III: steady state periodic forced response of rectangular plates », Journal of Sound and Vibration , vol. 264, n o 1, p. 1 ‑ 35, juin 2003, doi: 10.1016/S0022-460X(02)01162-8. [7] R. Benamar, M. M. K. Bennouna, et R. G. White, « The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part I: Simply supported and clamped-clamped beams », Journal of Sound and Vibration , vol. 149, n o 2, p. 179 ‑ 195, sept. 1991, doi: 10.1016/0022-460X(91)90630-3. [8] I. El Hantati, O. Outassafte, Y. El Khouddar, M. Belhaou, A. Adri, et R. Benamar, « 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 , vol. 23, p. 102822, sept. 2024, doi: 10.1016/j.rineng.2024.102822. [9] Y. El Khouddar, A. Adri, O. Outassafte, I. El Hantati, S. Rifai, et R. Benamar, « 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 , vol. 92, n o 9, p. 2767 ‑ 2784, sept. 2022, doi: 10.1007/s00419-022-02219-w. [10] O. Outassafte, A. Adri, Y. E. Khouddar, I. E. Hantati, S. Rifai, et R. Benamar, « Crack identification in circular arches through natural frequency variations and the firefly hybrid algorithm », Mechanics of Advanced Materials and Structures , vol. 31, n o 22, p. 5701 ‑ 5715, nov. 2024, doi: 10.1080/15376494.2023.2218857. [11] D. Q. Cao, M. T. Song, W. D. Zhu, R. W. Tucker, et C. H.-T. Wang, « Modeling and analysis of the in- plane vibration of a complex