VORTEX-INDUCED VIBRATIONS OF TWO SIDE-BY-SIDE EULER-BERNOULLI BEAMS

Vortex-induced vibration of two side-by-side elastic beams in a cross flow is numerically studied. The two beams are identical and fixed at both ends. In the numerical approach, the Euler–Bernoulli beam theory is used to model the beam vibration, and the laminar Navier–Stokes equations are solved to give the flow field. The flow equations are resolved using a finite element method and the flow-induced forces are calculated at every time step in order to correctly reflect the fluid–beam interaction. The beam response is calculated using the modal analysis method. Free vibrations of the two beams with three pitch ratios, T/D=1·13, 1·7 and 3·0, where T is the gap between the centers of the two beams and D is the beam diameter, are simulated at Re=800. Results obtained are compared with experimental measurements and other numerical results obtained assuming a two-degree-of-freedom (2-d.o.f.) model. The agreement is good in general. Correlation analysis is carried out, showing that the phase relation is different for differentT /D. The short-time Fourier transform (STFT) method is used to carry out the spectral analysis, along with the conventional auto-regressive moving averaging (ARMA) method for comparison. The STFT analysis shows that the time evolution of fluid force and beam vibration for T/D=1·13 and 3·0 are stationary. For theseT /D ratios, the STFT results are consistent with the ARMA results, but give a clearer picture of the higher order harmonics. For T/D=1·7, the time evolution is non-stationary. The STFT analysis shows that there are three types of frequency spectrum for the fluid force, with one, two, and three dominant frequencies respectively. The spectra intermittently change in a random way during the evolution. The ARMA results, though consistent with previous experiments, can only reveal a particular feature of the three different types of spectrum. This suggests that the STFT method is more appropriate to analyze the spectra of non-stationary time series in the study of flow-induced vibrations.