The mechanism of galloping control with a passive modal controller

Abstract

Passive modal controllers (PMC) are widely used in vibration control. However, the mechanism of PMC in galloping control is still unclear due to the limitation of the present quasi-steady theory. The motivation of this study is to reveal the dynamic mechanism of PMC in galloping control at a low Reynolds number ($Re$) via linear stability analysis (LSA) based on the unsteady aerodynamic model. The reduced-order model (ROM) of unsteady flow is identified using the autoregressive with exogenous input (ARX) technique based on the Navier–Stokes equations. Direct numerical simulations are utilized to support relevant results. It is found that the PMC transforms the unstable structural mode into the stable one due to the modal coupling effect. That is the reason for suppressing significant galloping vibration and eliminating the frequency lock-in phenomenon. The results obtained from dynamic mode decomposition (DMD) indicate that the PMC does not directly affect the unsteady vortex shedding, but changes the coupling mode and stability characteristics of the original coupled system. Thus, the second dominant mode of the flow field which is referred to as galloping mode is replaced with the second harmonic vortex shedding mode. Finally, a parametric study is conducted on the galloping control with a PMC from the perspective of system stability. The ROM-based LSA can provide the effective parameter range for PMC design.