PSI - Issue 83

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

296

amplitudes. The results demonstrate that appropriate placement of elastic supports combined with suitable material properties can significantly reduce nonlinear vibration levels and enhance the dynamic stability of cable-stayed beam systems. © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the ESIAM26 organizers

Keywords: Cable-stayed beam, Geometrically nonlinear vibrations, Elastic rotational supports, Multimodal analytical modeling, Free vibrations.

1. Introduction Cable-stayed beam structures are widely used in engineering applications such as bridges, towers, and lifting systems due to their structural efficiency and adaptability (see Fig. 1). Their dynamic behavior is governed by strong beam–cable coupling, leading to complex nonlinear responses. In this context, beam–cable interaction plays a dominant role in system dynamics (Cong et al., 2020), and is further confirmed as a key factor controlling nonlinear vibration behavior (Rjilatte et al., 2024a). The vibration response is also significantly influenced by the distribution and stiffness of elastic supports (Berjal et al., 2024a), while their number and positioning affect linear dynamic characteristics (Berjal et al., 2024b). In addition, geometric nonlinearities and modal interactions contribute significantly to the overall response (Rjilatte et al., 2024b), and energy transfer mechanisms between beam and cables further influence system dynamics (Kang et al., 2022). Regarding nonlinear analysis, amplitude-dependent behavior and modal interactions are highlighted in (El Kadiri et al., 2002); then, the Benamar approach is introduced for large-amplitude analysis (Moussaoui et al., 2000), and subsequently applied to capture geometric nonlinear effects (El Bikri et al., 2003). This framework is further extended to include multimode interactions (Bennouna and White, 1984), as well as nonlinear coupling and internal resonance effects (“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.), and is finally shown to be effective in describing higher-mode interactions (Berjal et al., 2026). More recently, optimization and identification techniques have been emphasized for complex structural systems (Outassafte et al., 2024), while improved computational strategies enhance vibration prediction accuracy (El Hantati et al., 2024). Parametric analyses further underline the role of structural configuration and boundary conditions (El Khouddar et al., 2022). Based on these developments, this work investigates the nonlinear dynamic response of cable-stayed beams, with a particular focus on the optimization of elastic support stiffness and their mechanical properties. The originality of this work lies in the combined investigation of elastic support parameters and material properties on the nonlinear vibration behavior using a multimode analytical formulation. Nomenclature Total length of the beam Global longitudinal coordinate along the beam ௜ Local coordinate of beam segment ௖௝ Local coordinate along cable ௖௝ Length of cable j ௝

Inclination angle of cable j ௝ Beam–cable connection point ௕ Young’s modulus of the beam ௕ Second moment of area of the beam ௕ Cross-sectional area of the beam ௖ Young’s modulus of the cable ௖ Cross-sectional area of the cable Excitation frequency