PSI - Issue 78

Ettore Sorge et al. / Procedia Structural Integrity 78 (2026) 1863–1870

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Figure 1. Scheme and idealization of the WTG: (a) schematic representation under W+E loads, and (b) WTG-HSFD components.

2.1. Structural Model The WTG-HSFD aero-elastic model was formulated as two explicitly coupled sub-systems — the WTG and the HSFD — thereby preserving the non-classical damping traits reported by (Gupta & Bose, 2017) while granting direct control over the damper’s energy -dissipation level. The WTG tower was discretised into beam elements whose nodal displacements (t) , velocities, and accelerations were assembled into the global vectors, see Eq. (1). Elemental mass ( ) , length ( ) , and elevation (ℎ ) data populated the diagonal translational matrix , whereas the consistent mass and stiffness matrices followed the procedure of (Di Paolo et al., 2021). Rayleigh damping with a uniform ratio = 1 % furnished the non-proportional viscous matrix , and the influence vectors , , and injected the aero-dynamic thrust ( ) , hub moment ( ) , and base acceleration ̈ ( ) into the translational equation of motion. Concurrently, the rotational degree of freedom ( ) of the HSFD obeyed Eq. (2), which balances the tower’s polar inertia , the velocity-dependent friction term sign( ̇( ))| ̇( )| , , the damper stiffness , and the gravity induced moment Σ ℓ (Sorge et al., 2024). By decoupling but synchronously solving the translational and rotational equations, the framework accommodates HSFD configurations of low, intermediate, or high dissipation without altering the baseline WTG damping, all while retaining computational efficiency. Non-linear inertial and geometric-stiffness contributions were omitted, consistent with prior evidence that their influence on global response is negligible for the loading regimes considered. ̈(t) + ̇(t) + (t) + D ( ) − D ̈( ) = ( ) + ( ) − ̈ ( ) (1) ̈( ) + sign( ̇( ))| ̇( )| , +( − ∑ ℓ =1 ) ( ) = M ( , (t), ̇(t)) (2) 3. Wind and Earthquake loads The NREL 5 MW WTG, conceived by the National Renewable Energy Laboratory, has emerged as a cornerstone against which novel turbine designs are evaluated under a spectrum of operating conditions. With a hub height of 90 m and a rotor diameter of 126 m, the machine maximizes energy capture through variable-speed operation and active pitch regulation; additional specifications appear in Table 1. Owing to its robust configuration and well-documented performance, the platform serves as a primary vehicle for research, design optimization, and techno-economic assessment across the wind-energy community. Figure. 1 (a) illustrates the turbine subjected concurrently to