Vibration analysis of cracked beams on elastic foundation using Timoshenko beam theory

Batıhan, Ali Çağrı
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.


Vibration Analysis of a Cracked Beam on an Elastic Foundation
Batihan, Ali Cagri; Kadıoğlu, Fevzi Suat (2016-06-01)
The transverse vibrations of cracked beams with rectangular cross sections resting on Pasternak and generalized elastic foundations are considered. Both the Euler-Bernoulli (EB) and Timoshenko beam (TB) theories are used. The open edge crack is represented as a rotational spring whose compliance is obtained by the fracture mechanics. By applying the compatibility conditions between the beam segments at the crack location and the boundary conditions, the characteristic equations are derived, from which the n...
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Citation Formats
A. Ç. Batıhan, “Vibration analysis of cracked beams on elastic foundation using Timoshenko beam theory,” M.S. - Master of Science, Middle East Technical University, 2011.