PSI - Issue 83

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

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Fig. 3. Normalized mode shapes corresponding to the first five vibration modes of the cable-stayed beam under simply supported (SS) boundary conditions.

The obtained mode shapes exhibit the expected structural behavior, characterized by an increasing number of zero-displacement points with the mode order. This consistency confirms the accuracy and robustness of the proposed formulation. Increase in E ୡ slightly increases natural frequencies, especially for lower modes. This effect decreases with increasing rotational stiffness.

Fig. 4. Effect of cable material properties, characterized by the Young’s modulus ௖ , on the natural frequencies under different rotational stiffness conditions. 3.2. Nonlinear vibration analysis This section addresses the nonlinear vibration behavior of the cable-stayed beam by considering geometric nonlinearities associated with large-amplitude oscillations. The analysis focuses on the combined influence of the end rotational stiffness and the maximum nondimensional displacement on the dynamic response. The evolution of the nonlinear frequency ratio and the corresponding curvature distributions are examined to highlight the effects of geometric nonlinearity. The results are compared with the linear case to emphasize the deviations induced by large displacements.