非线性元件次谐波运动的等效线性化

本文提出一个利用谐波平衡原理将非线性元件的作用力线性化的方法。非线性元件装于多自由度系统,系统在非线性元件处的运动含有与作用于系统的外谐和力非同步的分量。文中给出等效线性力参数的表达式,它们可通过一定的迭代步骤算出。文中以装有非同心型的挤压油膜阻尼器的不平衡刚性转子的次谐波响应为例,比较了用本文的方法与用Runge-Kutta法所得的计算结果。

EQUIVALENT LINEARIZATION OF A NONLINEAR ELEMENT WITH RESPECT TO SUBHARMONIC MOTIONS

This paper presents a linearization technique for nonlinear force by the methodof harmonic balance. The element which produces nonlinear force is incorporatedinto the multidegree-of-freedom system, the steady-state motions at the element have components that are non-synchronous with the external harmonic force exerted on the system. The equivalent force component is supposed to pe composedof two parts. The first part is the sum of an average force ,a linar spring force and a linear damping force just as in the case of linearization with respectto harmonic motions. The second part is the sum of the equivalent external harmonic forces having frequencies like those present in the non-synchronous motioncomponents at the element. The unknown parameters that characterize the equivalent force may be expressed analytically by the original nonlinear force and the assumed steady-state motion at the element, and may be evaluated by an iterativeprocedure. The technique is illustrated and tested for the sub-harmonic whirling of an unbalanced rigid rotor incorporating squeeze-film damper,without centralizing spring. The obtained results agree well with those from the full transientsolutions when using the Runge-Kutta method. But if the linearization technique is used,the computation time may be significantly reduced.