Quadratic Inverse Eigenvalue Problems : Theory , Methods , and Applications

QUADRATIC INVERSE EIGENVALUE PROBLEMS: THEORY, METHODS, AND APPLICATIONS Vadim Olegovich Sokolov, Ph.D. Department of Mathematical Sciences Northern Illinois University, 2008 Biswa Nath Datta, Director This dissertation is devoted to the study of quadratic inverse eigenvalue problems from theoretical, computational and applications points of view. Special attention is given to two important practical engineering problems: finite element model updating and substructured quadratic inverse eigenvalue problems. Because of their importance these problems have been well studied and there now exists a voluminous body of work, especially on finite element model updating, both by academic researchers and practicing engineers. Unfortunately, many of the existing industrial techniques are ad hoc in nature and lack solid mathematical foundation and sophisticated state-of-the-art computational techniques. In this dissertation, some of the existing engineering techniques and industrial practices have been explained, whenever possible, by providing mathematical explanations with the help of new results on the underlying quadratic inverse eigenvalue problems, and based on these results, new techniques of model updating and substructured quadratic inverse eigenvalue problems have been proposed. These results will contribute to advancement of the state-of-the-art knowledge in applied and computational mathematics, and mechanical vibrations and structural engineering. They will also impact the industries, such as automobile and aerospace companies, where these problems are routinely solved in their design and manufacturing. NORTHERN ILLINOIS UNIVERSITY DE KALB, ILLINOIS