Analytical and experimental study on Van der Pol-type and Rayleigh-type equations for modeling nonlinear aeroelastic instabilities

Abstract

An empirical modeling of nonlinear aerodynamic force during aeroelastic instabilities, that is, vortex-induced vibration (VIV), galloping and flutter, is necessary in the estimation of vibration responses. Previous works on single-degree-of-freedom (SDOF) models suggest that nonlinear forms (Van der Pol or Rayleigh types) differ from section to section, which causes difficulty in practical application. Analytical evidences in this study have clarified that Van der Pol-type and Rayleigh-type models are equivalent in the amplitude-dependent aerodynamic damping; their difference lies in the higher-order harmonic responses. An identification algorithm of aerodynamic parameters is proposed to improve the robustness of aerodynamic parameters and guarantee the equivalence of both model types. Wind-tunnel tests of typical aeroelastic instabilities indicate that higher-order harmonic responses are small for VIV, galloping, and early-stage flutter instability when compared with the fundamental components due to weak nonlinearity. Van der Pol-type and Rayleigh-type models are both applicable until the flutter amplitude grows excessively large. It is clear that both model types are suitable for any section shape when use the proposed method of aerodynamic identification, and thus can be treated as a universal model for estimating the vibration amplitudes of nonlinear aeroelastic instabilities.