Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed

Motivated by the well-known experiments of Tobias and Arnold (Proc. Inst. M ech. Engrs. 171 (1957) 669-690), we study the large-amplitude oscillations of an imperfect, flexible circular plate spinning near a critical speed res onance. A weakly non-linear theory for the transverse oscillations of the r otating, imperfect plate is derived and the near resonant response of a rep eated pair of backward and forward travelling waves is analysed. The experi mental results of Tobias and Arnold art: easily captured within the present analysis. In addition, several new dynamical phenomena are predicted as th e imperfection parameter is increased, such as emergence of pseudo-standing waves; their loss of stability through Hopf bifurcations leading to backwa rd and forward travelling waves with slow, periodically modulated amplitude s and phases period doubling sequences leading to Rossler-type chaotic attr actors and boundary crises phenomena; and emergence of isolas of steady wav e motions. Sufficiently high asymmetry can reduce by half, the vibration en ergy near resonant collapse phenomena. The results presented can provide gu idelines for designing imperfections in circular saws and hard disk drives to reduce vibrations near critical speed. (C) 2000 Elsevier Science Ltd. Al l rights reserved.