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 Functionally Graded Material Microbeam with Geometric Nonlinearity
Date
2017-02-02
Author
Uz, Canan
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
306
views
0
downloads
Cite This
In this paper, nonlinear vibration analysis of micro scale functionally graded material (FGM) beams with geometric nonlinearity due to large deflection is studied using modified couple stress theory (MCST). MCST is a nonlocal elasticity theory which includes a material length scale parameter since the size of an atomic microstructure becomes comparable to the length of the microbeam. Equations of motion of the micro scale FGM beam are obtained by using Hamilton's principle. Nonlinear free vibrations of the FGM microbeam with simply supported boundary conditions is investigated where the effect of the length scale parameter on the nonlinear natural frequencies of the microbeam is studied. The nonlinear partial differential equations of motion are converted into nonlinear ordinary differential equations by using Galerkin's Method. By using describing function method (DFM), a set of nonlinear algebraic equations are obtained which are solved by an iterative eigenvalue solver.
Subject Keywords
Functionally graded material microbeam
,
Modified couple stress theory
,
Euler-Bernoulli beam
,
Describing function method
,
Nonlinear natural frequency
URI
https://hdl.handle.net/11511/34788
DOI
https://doi.org/10.1007/978-3-319-54735-0_18
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 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...
Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach
Dağ, Serkan (2006-12-01)
A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to ha...
ELASTIC-PLASTIC STRESS ANALYSIS OF NONHOMOGENEOUS ROTATING SOLID DISCS
Eraslan, Ahmet Nedim; Gulgec, Mufit (2008-09-01)
A computational model is developed for the analysis of elastic and partially plastic stress states in functionally graded (FGM) variable thickness rotating solid disks. The modulus of elasticity, Poisson's ratio, uniaxial yield limit and density of the disk material are assumed to vary radially in any prescribed functional forms. Small deformations and a state of plane stress are presumed. Using the von Mises yield criterion, total deformation theory and a Swift-type nonlinear hardening law, a single nonlin...
Nonlinear vibration analysis of L-shaped beams and their use in vibration reduction
Ekici, Yiğitcan; Ciğeroğlu, Ender; Yazıcıoğlu, Yiğit; Department of Mechanical Engineering (2022-9)
In this thesis, nonlinear vibration analysis of both fixed L-shaped beam and L-shaped beam attached to a single degree of freedom (SDOF) system is performed for several cases with different structural parameters to observe the effect of these parameters. Then these beams are proposed to reduce the vibration amplitudes of certain structures, and the nonlinear effects on the dynamic responses of these structures are investigated. The nonlinear dynamic model of the L-shaped beam is obtained by using Euler-Bern...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
C. Uz and E. Ciğeroğlu, “Nonlinear Vibrations of a Functionally Graded Material Microbeam with Geometric Nonlinearity,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34788.
