Describing function method with balancing in time domain for 2-DOF airfoil system with nonlinear energy sink
A describing function method with balancing in time domain(DFBT)is used to efficiently solve 2-DOF airfoil system with nonlinear energy sink(NES).This method uses a set of basis func-tions to describe the periodic motion,discretes the dynamic equation in time domain and lists the equi-librium equation point by point to solve the basis function and obtain the harmonic coefficient.The point-by-point equilibrium equation obtained by discretization can provide overdetermined algebraic equations for solving harmonic coefficients,and the iterative convergence can be easily combined with minimum optimization.The method does not need to switch the time-domain and frequency-domain re-sponses of the nonlinear system frequently,which brings convenience to the solution.The results of the solution agree well with those of the numerical method,which verifies the effectiveness of the method.At the same time,due to the semi-analytic form of DFBT results,the unsteady solution of the flutter system and the complete subcritical bifurcation diagram can be obtained.Therefore,DFBT is suitable for solving the steady-state response of multi-degree-of-freedom flutter systems with complex nonlinearity.
nonlinear flutter systemlimit cyclenonlinear energy sinksemi-analytic method
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