采用时域平衡描述函数法求解含非线性能量阱的机翼颤振系统

Describing function method with balancing in time domain for 2-DOF airfoil system with nonlinear energy sink

采用一种时域平衡描述函数法(DFBT),高效求解含非线性能量阱(NES)的二元机翼颤振系统。该方法采用一组用于描述周期运动的基函数,在时域上将动力学方程离散并逐点列出平衡方程,以此求解出基函数的谐波系数。通过离散得到的逐点平衡方程提供超定代数方程组,结合最小值优化使得迭代容易收敛,从而实现谐波系数的求解。该方法无需对周期响应进行频繁的时频域转换,提高了计算效率。求解结果与数值方法的计算结果吻合良好,验证了方法的有效性。同时,由于DFBT结果具有半解析形式,可以得到颤振系统的非稳定解,获得了完整的亚临界分岔图。因此,DFBT适用于复杂非线性多自由度颤振系统的稳态响应求解。

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 functions to describe the periodic motion,discretes the dynamic equation in time domain and lists the equilibrium 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 responses 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.