Dynamic modeling and analysis of a spinning Rayleigh beam under deployment

Abstract

In this paper we propose a new model for a spinning beam under deployment and present analyses of the beam's dynamic responses and characteristics. The proposed model is established in an inertial reference frame by using the Rayleigh beam theory to consider the rotary inertia effect. This model is an advanced version of a model that we previously reported; that model was based on the Euler–Bernoulli beam theory, described in a rotating reference frame. We compare the dynamic responses and natural frequencies of a spinning beam under deployment between the proposed Rayleigh beam model and the previous Euler–Bernoulli beam model. In addition, we analyze the beat phenomena of a spinning Rayleigh beam under deployment in an inertial reference frame. Furthermore, we investigate the effects of the choice between the two reference frames (inertial and rotating reference frames) upon the analytical results for dynamic responses and natural frequencies. We show that the proposed model yields more accurate and reliable results for dynamic responses than the previous model, for the case in which a spinning beam is deployed.