Structural analysis of mistuned spatially periodic systems: A singular perturbation approach
Abstract
Structural systems with spatial symmetry are very often encountered in engineering practice. Typical examples of such systems include space platforms, multispan flexible continuous bridge structures, gas turbine engines, large space circular antennas and floppy disks in memory devices. These systems are usually analyzed by assuming some structural uniformity, often referred to in the literature as a "tuned" system condition. However, small nonuniformities inherent from practical realities that invariably arise due to manufacturing and material tolerances preclude the existence of such uniformity. These small nonuniformities or variations present in system parameters are commonly referred to as "structural mistuning". It has received wide attention in the vibration literature because of the fact that a small amount of mistuning under appropriate conditions can cause unexpectedly large amplitudes of vibration compared to those predicted on the basis of a perfectly tuned system. In this thesis, the dynamics of mistuned cyclic systems with special reference to strongly coupled bladed disk assemblies has been investigated. The analysis has utilized ideas from group representation theory, bifurcation theory, singular perturbation theory and modal analysis techniques. The general analysis methodology developed herein is applicable to any disk to which is attached a set of n blades which are strongly coupled cyclically, and mistuning or variations can arise in any of the system parameters. In particular, this study provides qualitative and, more importantly, quantitative information in the form of uniformly valid asymptotic expansions for the eigenfrequencies and the modal vectors of the structure. These expansions are used to describe the phenomena of eigenvalue curve veering modal rotations, and other manifestations of the sensitive dependence of eigenfunctions on system parameters which lead to modal bifurcations in the forced response of mistuned cyclic systems. Since this approach is general and systematic, the methodology developed here is also extended and applied to other discrete and continuous structures as well.
Degree
Ph.D.
Advisors
Bajaj, Purdue University.
Subject Area
Mechanical engineering
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