PSI - Issue 80

Francisco J.G. de Oliveira et al. / Procedia Structural Integrity 80 (2026) 1–10 Author name / Structural Integrity Procedia 00 (2023) 000–000

7

7

b)

a)

Fig. 5. Frequency-weighted PSD of the fluctuating deflection field, obtained through equation (2) for di ff erent spanwise positions, along θ α f ,α = − 45 ◦ , for FST cases 1 a and3 a .

Figure 5 illustrates that the spectral “energy” associated with cylinder deflection increases progressively toward the free end. Moving along the span, the structural response reaches larger amplitudes, culminating in enhanced deflection levels near the tip. Across all spectra, a peak at the vortex shedding frequency ( St ≈ 0 . 2) is evident, and its relative contribution grows when FST is introduced (Figure 5 b) ), as captured by fibres on both the windward and leeward sides. The amplification of the structural response at this frequency highlights the influence of FST on coherent vortex shedding, both by increasing the energy content of the shedding process and by enhancing its spanwise coherence (de Oliveira et al., 2025). This results in stronger contributions to the root bending moment. A comparable increase in spanwise correlation of vortex-induced structures under higher TI (%) was also reported by Maryami et al. (2020) for a 2D cylinder.

θ ± 45 ◦ f

θ ± 135 ◦ f

5

0 . 25 0 . 50 0 . 75 L 13 /D

4

3

E ∗ ( ε )

2

1

0

2

4

6

8

10

12

2

4

6

8

10

12

TI (%)

TI (%)

Fig. 6. Integration of the PSD of ε ′ over the vortex shedding frequency band.

To quantify the specific role of vortex shedding in driving the structural response, and respective interference between FST and the coherent flow structure, following Rind and Castro (2012) we define a relative energy measure:

E ∗ = ( E VS − E NOVS )

(4)

where E =

St VS +

St VS − E d ε ′ / d t ( y / D = 1 . 6) , d St . Here, E VS denotes the energy including the vortex shedding peak, while E NOVS excludes it, and St VS ± specify the frequency bounds of the shedding band. This metric, shown in Figure 6, reveals a clear positive correlation between turbulence intensity and E ∗ .