NONLINEAR TRANSVERSE VIBRATIONS AND STABILITY OF SPINNING DISKS WITH NONCONSTANT SPINNING RATE

This paper studies nonlinear transverse vibrations of spinning disks with nonconstant spinning rate. Here the angular speed of the disk is characterized as a small periodic perturbation superimposed upon a constant speed. Due to this perturbation in angular speed, nonautonomous terms appear in the equation of motion, which results in the existence of parametric instability. In this paper, Galerkin's method is first applied to yield a discretized system, and the method of multiple scales is used to obtain periodic solutions. All types of possible resonant combinations are investigated, and numerical results are shown for a simple harmonic speed perturbation.