多自由度强非线性颤振分析的增量谐波平衡法

对多个自由度上含有强非线性项系统的颤振问题，推广应用增量谐波平衡法进行分析．考虑带有强非线性立方平移和俯仰刚度项的二元机翼颤振方程，首先将方程用矩阵形式表示，然后把振动过程分解成为振动瞬态的持续增量过程，再采用振幅作为控制参数应用谐波平衡法，以这种推广的增量谐波平衡法求得方程解的表达式，并由此分析系统的分岔现象、极限环颤振现象和谐波项数的取值问题，最后用龙格-库塔数值方法进行验算，结果表明:分析多个自由度的强非线性颤振，增量谐波平衡法是精确有效的．

Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities

The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated bythe Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.