PSI - Issue 84

Gian Felice Giaccu et al. / Procedia Structural Integrity 84 (2026) 1055–1062 1057 1(b). The polar mass moments of inertia about the local axes [Fig. 1(a)] 1–1 and 2–2 are Ω,11 = Ω,22 = , with polar inertia about the spin axis 3–3 given by Ω, = Ω,11 + Ω,22 = Ω,TOT Ω2 , where Ω is the radius of gyration. The gyricity vector is then = Ω, , with the rotor angular velocity vector. The free-vibration dynamics of the two-DOF deck section model—comprising vertical and torsional motions [Fig. 1(b)]—are derived from the equilibrium of a lumped-parameter gyroscopic system with gyricity Ω (Giaccu and Caracoglia, 2021; Giaccu and Caracoglia, 2025). An additional rotational DOF about the vertical axis, , represents the relative motion between the rotor of the apparatus and the deck; it is modelled via a torsional spring of stiffness (Fig. 1b). The resulting lumped equations of motion for the gyroscopic unit are formulated for free vibrations. ( ) J J c k J c k                + + + =− + + =     (1) The parameter denotes the polar mass moment of inertia, while and are the viscous damping and elastic stiffness coefficients, corresponding to restoring forces and moments of the local degree of freedom ( , ) , i.e., the torsional deck rotation. The gyroscopic unit equation (replicating discrete mass and inertia) is combined with a continuous formulation of the deck loads (Giaccu and Caracoglia, 2021; Giaccu and Caracoglia, 2025). In Equation (1), the over-dots indicate time derivatives: total derivatives for the discrete DOF and partial derivatives for the continuous DOF ( , ) at the sectional coordinate where the unit is installed, e.g., ̇ = ∂ / ∂ . The parameters , , and represent the moment of inertia, torsional stiffness, and damping of the additional rotational DOF [Figs. 1(b)]. Equation (1) shows that the gyricity Ω couples the system’s degrees of freedom . 3. Wind Tunnel Experimental Study 3.1. Description of the Section Models and Setup This section outlines the experimental procedure carried out to evaluate the effectiveness of the proposed gyroscopic stabilizer (Fig. 2). The device was installed beneath the deck superstructure of a truss-type bridge section model, designed to replicate, as best as possible, the aeroelastic behavior of the Golden Gate Bridge (Jain, 1996; Jain et al., 1996; Jain et al., 1998). The principal geometric properties of the full-scale bridge are deck width of = 27.43 m and a central span length of ℓ=1263 m.

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Fig. 2. Schematics of the wind tunnel set up that replicates, as best as possible, the Golden Gate bridge section model: (a) cross-sectional view, (b) lateral close-up view of the aeroelastic force balance (measurements in millimeters).