The equivalent linearization method （ELM） is modified to investigate the nonlinear flut- ter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM...The equivalent linearization method （ELM） is modified to investigate the nonlinear flut- ter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flut- ter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation （LCO） is chosen as an active increment to produce bifurca- tion charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.展开更多
基金supported by the National Natural Science Foundation of China (Nos.:11002088,11172333,11272361)
文摘The equivalent linearization method （ELM） is modified to investigate the nonlinear flut- ter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flut- ter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation （LCO） is chosen as an active increment to produce bifurca- tion charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.
