强非线性颤振分析的一种改进的等效线性化法

分析了含三次强非线性俯仰刚度的二元机翼颤振系统。线性化俯仰方向的自由振动方程,用谐波平衡法求解该线性化方程,得到了改进的等效线性刚度。采用改进的等效刚度,应用等效线性化法得到了非线性颤振系统的分岔方程。算例表明,该方法提高了等效线性化法的精度。

An Improved Equivalent Linearization Method for Strongly Nonlinear Flutter Systems

The limit cycle flutter of a two-dimensional airfoil with a strongly cubic pitching stiffness is studied.The linearization method is used to linearize the free oscillating equation of the airfoil in the uncoupled pitching mode.The linearized equation is addressed by the harmonic balance method and the equivalent linear stiffness of the nonlinear stiffness is obtained.The attained equivalent stiffness is implemented in the equivalent linearizartion method of nonlinear flutter analysis and the bifurcation chart of the flutter system is obtained.Two numerical examples are taken as illustrations to validate the proposed method.It shows that the attained equivalent stiffness is in excellent agreement with the numerical solutions and it can improve the accuracy of the equivalent linearization method.In addition,it is quite intuitive to judge whether the bifurcation is supercritical or subcritical by the proposed method.