Nonlinear Free Vibration Analysis of Cable-Stayed Beam Using a Single-Mode Approach

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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. 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.