Resonance capture and targeted energy transfer for suppressing aeroelastic instability of 2-D wing

Abstract

Numerical simulations were conducted to study flow-induced vibration of a two-dimensional airfoil with two nonlinear energy sinks (NES). The relationship between targeted energy transfer (TET) and vibration suppression is analyzed in detail. The main system has two degrees of freedom – the pitch and heave. The two NES are treated as subsystems, in which the first NES is place at the leading edge and the second NES is placed at the trailing edge. The limit cycle oscillation (LCO), which is to be suppressed by the NES, is studied from the viewpoint of the TET. The resonance capture (RC) in the coupled nonlinear system is also discussed by the means of the energy and spectrum analysis. This is followed by a detailed target energy transfer discussion of the heave and pitch modes and the NES. In addition, the empirical mode decomposition (EMD) is utilized to obtain an intrinsic mode function (IMF) to analyze resonance capture in the system. The results show that the NES can absorb vigorous amount of energy from one of the specified vibration modes. As the RC occurs, the TET between the vibration modes in the coupled system becomes more significant. In particular, the TET between the NES and the wing becomes more efficient. This results in an increase in the critical freestream velocity as the NES suppresses the nonlinear vibration of the main system in a very effective way. As the total energy exceeds the suppression range of the subsystem, the NES loses its effectiveness on vibration suppression effect on the main system. The IMF of the EMD exhibits special super-harmonic resonance and frequency competition characteristics.