Vibrations of Circular Plates and Rotating Disks

Abstract

Introduction Rotating disks are the principal components of many engineering systems, such as hard-disk drives for computers (see Figure 12.1), optical memory disks (CD and DVD), circular saws and turbines. They can be conveniently modeled as circular and annular plates by using the nonlinear equations developed in Section 1.4 of this book. When a spinning disk is subjected to a transverse load, as in the case of a reading/writing head flying over a memory disk, the disk can experience a critical speed resonance with catastrophically large vibration amplitudes whenever the rotating speed is close to a certain multiple of a natural frequency of the disk. This explains the reason for the choice of operating disks at subcritical speeds. However, the necessity of faster data access rates in disk drives is increasing the speed of such devices; this justifies the nonlinear study developed here. In this chapter, the linear vibrations of fixed circular and annular plates is addressed first. Then, the nonlinear vibrations of free-edge circular plates is studied by using the von Karman equations of motion for circular plates. Finally, the problem of rotating clamped-free disks is solved. Literature review Linear vibrations of circular and annular plates are discussed in the book by Leissa (1969). Tobias (1957) and Williams and Tobias (1963) were among the first to study nonlinear undamped vibrations of imperfect and perfect circular plates.