基于增量谐波平衡法的杜芬方程非线性区间多值自动求解算法

Automatic Multivalue Algorithm of Nonlinear Interval of Duffing Equation Based on Incremental Harmonic Balance Method

以典型的非线性振动系统杜芬方程为例,研究应用增量谐波平衡法自动求解非线性方程区间内多值的问题。在非线性区间内选择一个与幅频特性曲线趋向相似的谐波项系数作为主动变量,根据振幅的变化情况,自动选择不同谐波项系数,直到求出所有的值,所求出的值与四阶Runge-Kutta法的结果相比精确度相当,验证了算法的正确性。

Taking the typical nonlinear vibration Duffing equation as an example,this paper studied the problem of solving multi-values of nonlinear equation intervals using the incremental harmonic balance（IHB）method.With a harmonic coefficient in the nonlinear interval as the active variable,which was similar to the tendency of the amplitude-frequency curve,different harmonic coefficients were automatically selected according to the change of amplitude,until all values were calculated.The calculated values were compared with the results obtained by four-order Runge-Kutta method.The results show that the two methods are equally precise,verifying the correctness of this algorithm.