PSI - Issue 83

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 83 (2026) 208–217

© 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; Single-mode approach; Modal analysis; Benamar method; Newton–Raphson method The displacement function is expanded in spatial and temporal series and then substituted into the expressions of the total kinetic and potential energies. Applying Hamilton’s principle leads to a nonlinear system, which is subsequently solved using Benamar’s method. Finally, the results are analyzed and discussed. The fourth European Conference on the Structural Integrity of Additively Manufactured Materials (ESIAM26) Nonlinear Free Vibration Analysis of Cable-Stayed Beam Using a Single-Mode Approach Mohamed Rjilatte a * , Ahmed Adri a , Omar Outassafte a , Yassine EL Khouddar b , ISSAM El Hantati c , Mohamed Berjal a , Rhali Benamar d a Laboratoire Procédé, Mécanique, Matériaux et Génie Idustrielle (LP2MGI), High School of Technology (ESTC), Hassan II University of Casablanca, Route d’El Jadida. Km 7, Oasis, Casablanca 8012, Morocco . b Equipe Modélisation et Optimisation des systèmes industriels MOSI-ENSAM-UMI. Meknes 4024, Morocco. c Laboratory for control and mechanical characterization of materials and structures (LCMCMS), National Higher School for Electricity and Mechanics (ENSEM), Hassan II University, Casablanca 8012 , Morocco. d Simulation Studies and Research Laboratory, Instrumentation and Measurements (LERSIM), Mohammadia School of Engineers (EMI), Mohammed V University, Rabat 10000, Morocco . Abstract This study investigates the geometric nonlinearity of large-amplitude vibrations of a beam suspended by symmetric cables using the single-mode approach. After establishing the equation of motion and applying the boundary and continuity conditions, the resulting homogeneous system is numerically solved using the Newton–Raphson method to determine the natural frequencies and linear displacements.

* Corresponding author.. E-mail address: mohamed.rjilatte.doc22@ensem.ac.ma

2452-3216 © 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 10.1016/j.prostr.2026.07.024