Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Vibration analysis of cracked beams on elastic foundation using Timoshenko beam theory
Download
index.pdf
Date
2011
Author
Batıhan, Ali Çağrı
Metadata
Show full item record
Item Usage Stats
68
views
34
downloads
Cite This
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.
Subject Keywords
Foundations
URI
http://etd.lib.metu.edu.tr/upload/12613602/index.pdf
https://hdl.handle.net/11511/21103
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Nonlinear Vibrations of a Beam with a Breathing Edge Crack Using Multiple Trial Functions
Batihan, Ali C.; Ciğeroğlu, Ender (2016-01-28)
In this paper, a beam like structure with a single edge crack is modeled and analyzed in order to study the nonlinear effects of breathing crack on transverse vibrations of a beam. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonl...
Theoretical Analysis of Open Spherical Microphone Arrays for Acoustic Intensity Measurements
Hacıhabiboğlu, Hüseyin (2014-02-01)
Acoustic intensity is a vectorial measure of acoustic energy flow through a given region of interest. Three-dimensional measurement of acoustic intensity requires special microphone array configurations. This paper provides a theoretical analysis of open spherical microphone arrays for the 3-D measurement of acoustic intensity. The calculations of the pressure and the particle velocity components of the sound field inside a closed volume are expressed using the Kirchhoff-Helmholtz integral equation. The con...
Investigation of tightly coupled arrays for wideband applications
Arda, Kaan; Dural Ünver, Mevlüde Gülbin; Department of Electrical and Electronics Engineering (2020-10)
This thesis aims to provide in depth research on tightly coupled dipole arrays to be used in ultrawideband apertures applications. First, operation principles of tightly coupled dipole arrays are investigated. Starting from the Wheeler’s current sheet aperture concept, some calculations on bandwidth and impedance concepts are conducted. B.A. Munk’s addition to the concept, use of capacitive elements between adjacent dipoles, are introduced. Array unit cell is modeled using equivalent circuit approach,...
Nonlinear Vibrations of a Beam with a Breathing Edge Crack
Batihan, Ali C.; Ciğeroğlu, Ender (2015-02-05)
In this paper, nonlinear transverse vibration analysis of a beam with a single edge crack is studied. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonlinear behavior due to opening and closing of the crack region. In this paper, a...
Study of modeling of water saturation in archie and non-archie porous media
Dalkhaa, Chantsalmaa; Okandan, Ender; Department of Petroleum and Natural Gas Engineering (2005)
The aim of this thesis is to study water saturation models available in the literature and to apply a proper one to a real field case. Archie equation is the most well-known water saturation model. However, it is formulated on some assumptions and is applicable to only clean sands. Archie equation cannot be used for shaly formation. There are many shaly water saturation models that account for shale effect for water saturation estimation. In this study, 3 wells, namely Well-01, Well-02 and Well-03 are studi...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.