Bifurcation analysis of a two-degree-of-freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation-incremental method

A perturbation-incremental (PI) method is presented for the computation, continuation and bifurcation analysis of limit cycle oscillations (LCO) of a two-degree-of-freedom aeroelastic system containing a hysteresis structural nonlinearity. Both stable and unstable LCOs can be calculated to any desired degree of accuracy and their stabilities are determined by the theory of Poincaré map. Thus, the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics, period-doubling, saddle-node bifurcation, Neimark-Sacker bifurcation and the coexistence of limit cycles. The dynamic response is quite different from that of an aeroelastic system with freeplay structural nonlinearity. New phenomena are observed in that the emanating branches from period-doubling bifurcations are not smooth and the bifurcation of a LCO may lead to the simultaneous coexistence of all period-2ⁿ LCOs.