# Modeling of vibration for functionally graded beams

Gülsemay Yiğit; Ali Şahin; Mustafa Bayram

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 661-672
- ISSN: 2391-5455

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topGülsemay Yiğit, Ali Şahin, and Mustafa Bayram. "Modeling of vibration for functionally graded beams." Open Mathematics 14.1 (2016): 661-672. <http://eudml.org/doc/286767>.

@article{GülsemayYiğit2016,

abstract = {In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.},

author = {Gülsemay Yiğit, Ali Şahin, Mustafa Bayram},

journal = {Open Mathematics},

keywords = {Adomian decomposition method; Functionally graded beam; Fourier analysis; Orthogonality; Fourier series expansion method; mixture rate for the material},

language = {eng},

number = {1},

pages = {661-672},

title = {Modeling of vibration for functionally graded beams},

url = {http://eudml.org/doc/286767},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Gülsemay Yiğit

AU - Ali Şahin

AU - Mustafa Bayram

TI - Modeling of vibration for functionally graded beams

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 661

EP - 672

AB - In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

LA - eng

KW - Adomian decomposition method; Functionally graded beam; Fourier analysis; Orthogonality; Fourier series expansion method; mixture rate for the material

UR - http://eudml.org/doc/286767

ER -

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