Dynamic modeling and analysis of a spinning beam with an axial motion

Abstract

In chapter 2, the nonlinear lateral vibrations of a beam deploying from a fixed rigid hub are analysed when the beam has a spinning motion. Previous studies do not consider the nonlinear coupled effect between axial and lateral displacements when analysing the vibration behaviour of a deploying beam with spin. In contrast, the present study considers the nonlinear coupling effect of the axial and lateral displacements for a deploying beam with spin to investigate the vibration behaviour more exactly and comprehensively. The Euler-Bernoulli beam and von Karman nonlinear strain theory are used together to develop a new nonlinear model. The differences in dynamic response between the linear and nonlinear models are compared, and the effects of physical parameters on the differences are investigated. In addition, the beat phenomenon of a deploying beam with spin is studied. In chapter 3, I propose a new model for a spinning beam with 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 I previously studied in chapter 2, which is based on the Euler-Bernoulli beam theory, described in a rotating reference frame. I compare the dynamic responses and natural frequencies of a spinning beam with deployment between the proposed Rayleigh beam model and the previous Euler-Bernoulli beam model. In addition, I analyze the beat phenomena of a spinning Rayleigh beam with deployment in an inertial reference frame. Furthermore, I 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. It is shown 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. In chapter 4, the vibration and stability of a simply supported axially moving beam are analysed when the beam has a spinning motion. When an axially moving beam has a spinning motion, the rotary inertia plays important role on the lateral vibration. In previous studies, existing rotary inertia terms are inconsistent and some important rotary inertia terms induced by the moving and spinning motions are missing because the kinetic energies are not exactly derived. In contrast, the present study adopts the Rayleigh beam theory and derives more exact kinetic energy and equation of motion from a position vector. The rotary inertia terms derived by the present study are compared with those of the previous studies. The differences in the natural frequencies and dynamic responses between the present and previous models are investigated. In addition, the stability region and border for the combination of the moving and spinning speeds are also studied. Computations of the natural frequencies and dynamic responses show that the present equation of motion is more reliable than those of the previous models of the simply supported axially moving beams with spin because the present model fully considers the rotary inertia terms.