Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
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
Nonlinear Vibrations of a Beam with a Breathing Edge Crack Using Multiple Trial Functions
Date
2016-01-28
Author
Batihan, Ali C.
Ciğeroğlu, Ender
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
240
views
0
downloads
Cite This
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 nonlinear behavior due to opening and closing of the crack region. In this paper, partial differential equation of motion obtained by Euler-Bernoulli beam theory is converted into nonlinear ordinary differential equations by using Galerkin's method with multiple trial functions. The nonlinear behavior of the crack region is represented as a bilinear stiffness matrix. The nonlinear ordinary differential equations are converted into a set of nonlinear algebraic equations by using harmonic balance method (HBM) with multi harmonics. Under the action of a harmonic forcing, the effect of crack parameters on the vibrational behavior of the cracked beam is studied.
Subject Keywords
Breathing crack
,
Euler-Bernoulli beam
,
Galerkin's method
,
Harmonic balance method
,
Nonlinear vibrations
URI
https://hdl.handle.net/11511/36618
DOI
https://doi.org/10.1007/978-3-319-29739-2_1
Collections
Department of Mechanical Engineering, Conference / Seminar
Suggestions
OpenMETU
Core
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...
Nonlinear Transverse Vibrations of a Beam with Multiple Breathing Edge Cracks
Batihan, Ali C.; Ciğeroğlu, Ender (2017-02-02)
One step beyond the studies of transverse vibration of beams with a breathing edge crack is the verification of the theoretical crack beam models with an experimental test set up. Beams with a single breathing edge crack can be used as a specimen for the experimental test. However, there is no assurance against the unexpected additional cracks in the specimens, whichmay cause unexpected results. Therefore, in this paper nonlinear transverse vibration of a beam with multiple breathing edge cracks is consider...
Nonlinear Vibration Analysis of Uniform and Functionally Graded Beams with Spectral Chebyshev Technique and Harmonic Balance Method
Dedekoy, Demir; Ciğeroğlu, Ender; Bediz, Bekir (2023-01-01)
In this paper, nonlinear forced vibrations of uniform and functionally graded Euler-Bernoulli beams with large deformation are studied. Spectral and temporal boundary value problems of beam vibrations do not always have closed-form analytical solutions. As a result, many approximate methods are used to obtain the solution by discretizing the spatial problem. Spectral Chebyshev technique (SCT) utilizes the Chebyshev polynomials for spatial discretization and applies Galerkin's method to obtain boundary condi...
Nonlinear vibration analysis of functionally graded beams
Dedeköy, Demir; Ciğeroğlu, Ender; Bediz, Bekir; Department of Mechanical Engineering (2022-8)
In this thesis, nonlinear forced vibrations of functionally graded (FG) Euler-Bernoulli Beams are studied. Two types of nonlinearities, large deformation nonlinearity and nonlinearities resulting from rotating beam dynamics, are considered. The Spectral Chebyshev Technique (SCT) is employed for solving governing equations of the spectral-temporal boundary value problems of beam vibrations, which do not always have closed-form analytical solutions. The SCT is combined with Galerkin’s method to obtain spatial...
Nonlinear 3D Modeling and Vibration Analysis of Horizontal Drum Type Washing Machines
Baykal, Cem; Ciğeroğlu, Ender; Yazıcıoğlu, Yiğit (2020-01-01)
In this study, a nonlinear 3-D mathematical model for horizontal drum type washing machines is developed considering rotating unbalance type excitation. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM). The resulting nonlinear algebraic equations are solved by using Newton’s method with arc-length continuation. Several case studies are performed in order to observe the effects of orientation angles of springs and damp...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. C. Batihan and E. Ciğeroğlu, “Nonlinear Vibrations of a Beam with a Breathing Edge Crack Using Multiple Trial Functions,” 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36618.