Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering

First Advisor

James E. Bernard


Determining the natural frequencies and mode shapes is an important step in the design of physical systems. Typically for large systems, a model is prepared using a finite-element preprocessor, an eigenvalue problem is formed, and an eigenvalue solver is used to obtain the natural frequencies and mode shapes. If modification of the design is needed to bring the natural frequencies and mode shapes within design guidelines, then a re-solution of the eigenvalue problem is required. Frequently, the iterative nature of the re-solution lends itself to solution using structural optimization methods where the eigenvalue problem becomes part of the objective function subject to various design constraints;The design constraints are often interdependent and rarely subject to absolute limits. Only by including the designer in the optimization process can these constraints be re-evaluated during the optimization process and their relative importance in specific cases be adjusted. In addition, for large systems, each re-solution is computationally intensive and time consuming. It is therefore advantageous to use an estimate of the eigenvalues and eigenvectors of the system for purposes of structural optimization;This thesis presents several methods of estimating vibration frequencies and mode shapes in an effort to minimize the computational burden of dynamic analysis re-design. The goal is to provide a method for estimating frequencies and mode shapes for systems subject to large design changes in order to facilitate interactive participation of the designer in the optimization process. A case is also made for combining the proposed methodology with high-level computer graphics to provide an interactive, graphical tool for designers of physical systems.



Digital Repository @ Iowa State University,

Copyright Owner

Judith Marie Callicott Vance



Proquest ID


File Format


File Size

81 pages