增量谐波平衡法在分段结构非线性气动弹性系统的求解

本文将增量谐波平衡法推广至分段结构非线性气动弹性系统的周期响应分析中。对分段结构非线性气动弹性方程,推导其增量谐波平衡过程,研究了分段非性项的处理方法,实现了非线性气动弹性方程到线性化代数方程组的转化,可以为其它的分段非线性的处理提供思路。为了加快本文方法的收敛过程,通过对数值解进行快速傅立叶变换,获得响应中的主导频率成分,避免了盲目地对系统解形进行假设,最终可以快速地获得了响应近似周期解。与数值结果进行对比,验证了本文求解方法的正确性,同时讨论了谐波项数对解的精度的影响以及间隙和刚度比对响应幅值的影响。基于增量谐波平衡法可以快速地获得分段结构非线性气动弹性系统的响应,拓展了增量谐波平衡法的应用范围。

Study on Incremental Harmonic Balance Approach forPiecewise Structural Nonlinear Aeroelastic System

The incremental harmonic balance method is extended to analysis of the periodic responses of piecewise structural nonlinear aeroelastic system. The process of incremental harmonic balance method is derived for the nonlinear aeroelastic system. The nonlinear terms are studied and the conversion of the nonlinear aeroelastic equation to a linear algebraic one are established, which can provide a idea to other piecewise nonlinearity. To accelerate the convergence, Fast Fourier Transform is perform on the numerical solution to extract the dominant frequency, which can avoid the blind assumption of the solution.. Finally, the periodic responses are obtained. The comparison with the numerical solution verifies the correctness. The effect of the numbers of harmonics on the solution precision as well as the effect of the free-play and stiffness ratio on the response amplitude is discussed. The incremental harmonic balance approach is very effective for piecewise structural nonlinear aeroelastic system, and its application is expanded.