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Abstract

This thesis presents an analysis of the vibration and stability characteristics of rotating strings and disks at supercritical speeds. The dynamic interactions between an idealized rotating circular string and a stationary constraint consisting of a spring, a damper, a mass or a frictional restraint are studied. The method of traveling waves is applied to develop the characteristic equation. The physics of the interactions between the string and the restraints are discussed in depth. The nonlinear vibrations of an elastically-constrained rotating string are investigated. The nonlinearities of the string deformation and the spring stiffness are considered. Butenin’s method is adopted to develop a closed-form analytical solution for single-mode oscillations of the system. The analysis shows that the geometric nonlinearity restrains the flutter instability of the string at supercritical speeds. The effects of rigid-body motions on free oscillations of an elastically-constrained rotating disk are studied. The coupling between the translational rigid-body motion and the flexible body deformation is shown to reduce the divergence instability of the disk, but the tilting rigidbody motion does not change the stability characteristics. An analysis of nonlinear vibrations of an elastically-constrained rotating flexible disk is developed. The equations of motion are presented by using von Karman thin plate theory. The stress function is analytically solved by assuming a multi-mode transverse displacement field. The study shows that the geometric nonlinearity generates hardening effects on the dynamics of a rotating disk, and the unbounded motions at divergence and flutter speeds predicted by the existing linear analyses do not take place because of the large-amplitude vibrations.