"This thesis develops perturbation series solutions for the eigenvalues and eigenvectors of nonclassically damped dynamic systems for the case where the unperturbed system has repeated eigenvalues. The case of repeated eigenvalues is much more complicated than the case of perturbing a system with distinct eigenvalues. Because of this difficulty, only a specific category of dynamic systems with repeated eigenvalues is addressed. Namely, only those systems that when perturbed have series solutions of the form of a power series. This category of systems can be easily identified by an a priori check developed in the application section of this thesis. The issue of existence and convergence of the series solutions is also addressed. To adequately present and defend the above material, the perturbation theory of linear operators is discussed.
The more abstract case of defective systems is also discussed in the context of solving such systems with the Puiseux series.
The application section of this thesis presents a second order solution for a nonclassically damped system. It demonstrates the application of the convergence condition for the case of repeated eigenvalues and also demonstrates the a priori check that verifies the correctness of a power series solution.
Also as a part of this thesis a paper is presented on the series solution of gyroscopic systems with nonclassical damping. This paper develops a series solution for damped gyroscopic system. Also the convergence condition of Peres-Da-Silva et al. is modified to be applicable to gyroscopic systems"--Abstract, page iv.
Randolph, Timothy W.
Mechanical and Aerospace Engineering
M.S. in Engineering Mechanics
University of Missouri--Rolla
Journal article titles appearing in thesis/dissertation
Eigenvalue and Eigenvector Determination for Damped Gyroscopic Systems
viii, 75 pages
© 1995 Daniel Patrick Malone, All rights reserved.
Thesis - Open Access
Print OCLC #
Link to Catalog Record
Malone, Daniel Patrick, "Eigenproperties of nonclassically damped dynamic systems" (1995). Masters Theses. 1469.