In this thesis, transverse vibration of a cracked beam on an elastic foundation and
the effect of crack and foundation parameters on transverse vibration natural
frequencies are studied. Analytical formulations are derived for a beam with
rectangular cross section. The crack is an open type edge crack placed in the
medium of the beam and it is uniform along the width of the beam. The cracked
beam rests on an elastic foundation. The beam is modeled by two different beam
theories, which are Euler-Bernoulli beam theory and Timoshenko beam theory.
The effect of the crack is considered by representing the crack by rotational
springs. The compliance of the spring that represents the crack is obtained by
using fracture mechanics theories. Different foundation models are discussed / these models are Winkler Foundation, Pasternak Foundation, and generalized
foundation. The equations of motion are derived by applying Newton' / s 2nd law on
an infinitesimal beam element. Non-dimensional parameters are introduced into
equations of motion. The beam is separated into pieces at the crack location. By
applying the compatibility conditions at the crack location and boundary
conditions, characteristic equation whose roots give the non-dimensional natural
frequencies is obtained. Numerical solutions are done for a beam with square
cross sectional area. The effects of crack ratio, crack location and foundation
parameters on transverse vibration natural frequencies are presented. It is
observed that existence of crack reduces the natural frequencies. Also the elastic
foundation increases the stiffness of the system thus the natural frequencies. The
natural frequencies are also affected by the location of the crack.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12613602/index.pdf |
| Date | 01 September 2011 |
| Creators | Batihan, Ali Cagri |
| Contributors | Kadioglu, Suat |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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