Modeling for transient and modal analysis of a flexible beam attached to a rigid shaft undergoing free rotational motion considering two-way inertia coupling

Abstract

A novel linear dynamic model is proposed for the transient and modal analyses of a flexible beam attached to a rigid shaft undergoing free rotational motion. For the proposed modeling of the shaft-beam coupled system, the shaft angular speed is modeled as the sum of a reference angular speed and generalized speed instead of the time derivative of the shaft rotation angle which has traditionally been used for the shaft dynamic modeling. Thus, the shaft-beam coupled system is linearized around the reference angular speed for deriving the equations of motion. With the proposed modeling method, the two-way inertia coupling effect between the rigid shaft and flexible beam can be considered accurately. The transient responses obtained with the proposed model are in good agreement with those obtained with a nonlinear dynamic analysis program. Moreover, due to the linearity of the proposed dynamic model, modal characteristics of the shaft-beam coupled system can be also accurately identified.