Esta Kägo will defence her doctoral thesis "Natural vibrations of elastic stepped plates with cracks" in order to gain the degree of doctor of philosophy in mathematics on the 28 August 2013 at 12.15 in the faculty of mathematics and computer science of the University of Tartu, J. Liivi St 2, room 403.
Supervisor: Jaan Lellep (professor, TÜ matemaatika instituut)
Professor Aleksander Klauson (Tallinn Technical University) Professor Evgeny Barkanov (Riga Technical University)
To assess structural durability non-destructive methods are used. These allow to detect defects in structures without destroying them in the process. There are many non-destructive methods, one of them is the eigenfrequency method, which is based on the property of the structures to oscillate freely at certain frequencies. These frequencies are called eigenfre-quencies. Theoretical investigation eigenfrequencies of the structures is the main topic of this dissertation.
This dissertation examines eigenfrequencies of two types of stepped structures, namely plates and plate strips. The main question is how the cracks affect the eigenfrequencies of these structures. We consider cracks that are stable, have constant length and are located at the re-entrant corners of steps of the structures. This work can be divided into three parts. In the first section the impact of cracks on the eigenfrequencies of isotropic plate strips under different boundary conditions is examined. The second section is devoted to the role of cracks in anisotropic plates. The third section deals with the cracked anisotropic plates resting on elastic foundation.
In the dissertation a new analytical method, which combines the classical theory of plates and the equations of fracture mechanics is proposed. The proposed method is the first analytical method that allows us to model eigenfrequencies of cracked and stepped structures at the same time.