| Summary: | 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. === Applied Science, Faculty of === Mechanical Engineering, Department of === Graduate
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