Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.
Hydrodynamic Modeling and Design of Robotic Fish using Slender Body Theory
