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.