The effect of mass ratio and spring stiffness on flow-induced vibration of a square cylinder at different incidence angles

This paper presents a numerical study of the effect of spring stiffness and mass ratio on flow-induced vibration (FIV) of a square cylinder placed at four different incidence angles: α = 0 ∘ , 10 ∘ , 22 . 5 ∘ , 45 ∘ . The FIV is dominated by vortex-induced vibration (VIV), while another common form of FIV, galloping, is only found at α = 0 ∘ . A period-doubled mode which has a half of the shedding frequency of a fix body frequency component is found in all incidence angles except 0 ∘ . For these cases of α = 22. 5 ∘ ,4 5 ∘ , there exists a limiting mass ratio beyond which period-doubled does not exist. However, all mass ratio has a period-doubled mode at α = 10 ∘ due to its high asymmetry. The parameter of effective elasticity k e f f 1 ∗ combined by mass ratio and spring stiffness is introduced in this paper. For the period-double mode and galloping, another effective elasticity k e f f 0.5 ∗ related to half of the frequency of a fix body is needed. The results show that the different flow regimes is a function of the effective elasticity rather than the reduce velocity with the change of mass ratio and spring stiffness. By using the effective elasticity, the limited mass ratio for occurrence of galloping can be determined.