PSI - Issue 83

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

297

଴ Reference linear natural frequency ௟ ∗ Nondimensional linear natural frequency ௡∗ ௟ Nondimensional nonlinear natural frequency ௠∗ ௔௫

Maximum nondimensional transverse vibration amplitude

2.Method 2.1. Linear formulation

The present study develops a simplified structural model of a cable-stayed bridge deck, modeled as a continuous beam supported by multiple inclined cables (Fig. 2). The beam, simply supported at both ends, rests on elastic supports in both translational and rotational directions, characterized by the stiffnesses ் ௜ and ఏ௜ , respectively. The beam–cable connection points divide the deck into several segments, each considered as an independent beam element within the framework of the static and dynamic analysis.

Fig. 1. Examples of cable-stayed beam structures observed in practice. The static equilibrium configuration is described through the cable displacements ௖௝ , ௖௝ , ௖௝ and the transverse displacements of the beam ௕௜ . Each cable is assumed to follow a parabolic profile given by ௖௝ ൌ4 ௖௝ ሾ ݔ ௖௝ / ௖௝ െ ሺ ݔ ௖௝ / ௖௝ ሻ ଶ ሿ , where the sag-to-span ratio ௖௝ / ௖௝ remains below 1/10.

Fig. 2. Structural configuration of a cable-stayed beam supported by multiple inclined cables and elastic supports.

The pylons supporting the cables are assumed to be rigid, since previous experimental and numerical investigations have shown that their vibration amplitudes remain negligible. Owing to the high axial stiffness of the beam ( ௕ ௕ / ௕ ൐൐48 ௕ ௕ / ௕ଷ ), axial deformations are neglected. In addition, the horizontal component of the cable tension is considered to have a limited effect on the global response and is therefore omitted, in line with the assumptions reported by (Cong et al., 2020). Based on these considerations, Hamilton’s principle is applied to establish the governing equations of coplanar motion, after reducing the structural model accordingly.