Modeling of vibration for functionally graded beams
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 an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-01-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2016-0057 |
| _version_ | 1818720369052221440 |
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| author | Yiğit Gülsemay Şahin Ali Bayram Mustafa |
| author_facet | Yiğit Gülsemay Şahin Ali Bayram Mustafa |
| author_sort | Yiğit Gülsemay |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T20:21:44Z |
| format | Article |
| id | doaj.art-b9256ff26ca74b3a81120ada008fe1b1 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T20:21:44Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-b9256ff26ca74b3a81120ada008fe1b12022-12-21T21:33:55ZengDe GruyterOpen Mathematics2391-54552016-01-0114166167210.1515/math-2016-0057math-2016-0057Modeling of vibration for functionally graded beamsYiğit Gülsemay0Şahin Ali1Bayram Mustafa2Department of Electrical and Electronics Engineering, Istanbul Kemerburgaz University, Istanbul, TurkeyVodno Consultancy, 1000 Skopje, Macedonia (the former Yugoslav Republic of)Department of Computer Engineering, Istanbul Gelisim University, Istanbul, TurkeyIn 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.https://doi.org/10.1515/math-2016-0057adomian decomposition methodfunctionally graded beamfourier analysisorthogonality35l3574k10 |
| spellingShingle | Yiğit Gülsemay Şahin Ali Bayram Mustafa Modeling of vibration for functionally graded beams Open Mathematics adomian decomposition method functionally graded beam fourier analysis orthogonality 35l35 74k10 |
| title | Modeling of vibration for functionally graded beams |
| title_full | Modeling of vibration for functionally graded beams |
| title_fullStr | Modeling of vibration for functionally graded beams |
| title_full_unstemmed | Modeling of vibration for functionally graded beams |
| title_short | Modeling of vibration for functionally graded beams |
| title_sort | modeling of vibration for functionally graded beams |
| topic | adomian decomposition method functionally graded beam fourier analysis orthogonality 35l35 74k10 |
| url | https://doi.org/10.1515/math-2016-0057 |
| work_keys_str_mv | AT yigitgulsemay modelingofvibrationforfunctionallygradedbeams AT sahinali modelingofvibrationforfunctionallygradedbeams AT bayrammustafa modelingofvibrationforfunctionallygradedbeams |