Research Article
Fonksiyonel derecelendirilmiş sandviç kirişlerin Navier yöntemiyle serbest titreşim ve burkulma analizi
Abstract
Bu çalışmada, fonksiyonel
derecelendirilmiş (FDM) sandviç kirişlerin serbest titreşim ve burkulma
analizleri Navier tipi çözüm yöntemi ile incelenmiştir. Yer değiştirme alanı,
birinci mertebeden kayma deformasyonlu kiriş teorisine göre ifade edilmiş,
Lagrange prensibi kullanılarak hareket denklemleri elde edilmiştir. Hacimsel
seramik oranı bir kuvvet fonksiyonu şeklinde tanımlanmıştır. Analitik çözümde
göz önüne alınan her sınır şartı için farklı trigonometrik fonksiyonlar
kullanılmıştır. Çalışmada, a) homojen seramik çekirdek ve FDM yüzeylerden
oluşturulan sandviç kiriş (Tip A) ve b) FDM çekirdek ve homojen yüzeylerden
oluşturulan sandviç kiriş (Tip B) olmak üzere iki tip kiriş ele alınmıştır.
Çeşitli sınır şartları, ortamdaki seramik oranları ve narinlik oranı için doğal
frekanslar ve burkulma yükleri sayısal olarak hesaplanmıştır. Sayısal sonuçlar
literatürdeki mevcut çalışmaların sonuçları ile karşılaştırılmış ve son derece
uyumlu oldukları görülmüştür.
Keywords
Fonksiyonel derecelendirilmiş malzeme sandviç kiriş Navier yöntemi birinci mertebeden kayma deformasyonlu kiriş teorisi serbest titreşim burkulma
References
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- Alshorbagy, A. E., Eltaher, M. A. ve Mahmoud, F. F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35,1, 412-425, 2011.
- Vo, T. P., Thai, H.-T., Nguyen, T.-K., Maheri, A. ve Lee, J., Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory, Engineering Structures, 64, 12-22, 2014.
- Kahya, V. ve Turan, M., Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory, Composites Part B: Engineering, 109, 108-115, 2017.
- Kahya, V. ve Turan, M., Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element, Composites Part B: Engineering, 146, 198-212, 2018.
- Aria, A.I. ve Friswell, M.I., A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites Part B: Engineering, 166, 233-246, 2019.
- Mollamahmutoğlu, Ç. ve Mercan, A., A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory, Composite Structures, 233, 1-15, 2019.
- Sankar, B.V., An elasticity solution for functionally graded beams, Composite Science and Technology, 61, 689-696, 2001.
- Aydogdu, M. ve Taskin, V., Free vibration analysis of functionally graded beams with simply supported edges, Materials & Design, 28,5, 1651-1656, 2007.
- Sina, S. A., Navazi, H. M. ve Haddadpour, H., An analytical method for free vibration analysis of functionally graded beams, Materials & Design, 30,3, 741-747, 2009.
- Pradhan, K. K. ve Chakraverty, S., Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method, Composites Part B: Engineering, 51, 175-184, 2013.
- Öktem, A. S., Fonksiyonel derecelendirilmiş (FD) ileri kompozit plakların statik analizi, Journal of the Faculty of Engineering and Architecture of Gazi University, 29, 111-119, 2014.
- Nguyen, T.-K. ve Nguyen, B.-D., A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams, Journal of Sandwich Structures & Materials, 17,6, 613-631, 2015.
- Chen, W. R. ve Chang, H., Closed-form solutions for free vibration frequencies of functionally graded Euler-Bernoulli beams, Mechanics of Composite Materials, 53,1, 79-98, 2017.
- Lee, J. W. ve Lee, J. Y., Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122, 1-17, 2017.
- Turan M., Tabakalı kirişlerin static, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli, Doktora Tezi, Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon, 2018.
- Sayyad, A.S. ve Ghugal, Y.M., Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams, Asian Journal of Civil Engineering, 19, 607-623, 2018.
- Sayyad, A.S. ve Avhad, P.V., On static bending, elastic buckling and free vibration analysis of symmetric functionally graded sandwich beams, Journal of Solid Mechanics, 11, 166-180, 2019.
- Lee, J. W. ve Lee, J. Y., Contribution rates of normal and shear strain energies to the natural frequencies of functionally graded shear deformation beams, Composites Part B: Engineering, 159, 86-104, 2019.
Year 2021,
Volume: 36 Issue: 2, 743 - 758, 05.03.2021
Abstract
References
- Yıldırım, B., Fonksiyonel derecelendirilmiş malzemeden yapılmış kenar çatlaklı bir tabakada ısıl şok kırılmasının sonlu elemanlar metodu ile incelenmesi, Journal of the Faculty of Engineering and Architecture of Gazi University, 19, 235-245, 2004.
- Alshorbagy, A. E., Eltaher, M. A. ve Mahmoud, F. F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35,1, 412-425, 2011.
- Vo, T. P., Thai, H.-T., Nguyen, T.-K., Maheri, A. ve Lee, J., Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory, Engineering Structures, 64, 12-22, 2014.
- Kahya, V. ve Turan, M., Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory, Composites Part B: Engineering, 109, 108-115, 2017.
- Kahya, V. ve Turan, M., Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element, Composites Part B: Engineering, 146, 198-212, 2018.
- Aria, A.I. ve Friswell, M.I., A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites Part B: Engineering, 166, 233-246, 2019.
- Mollamahmutoğlu, Ç. ve Mercan, A., A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory, Composite Structures, 233, 1-15, 2019.
- Sankar, B.V., An elasticity solution for functionally graded beams, Composite Science and Technology, 61, 689-696, 2001.
- Aydogdu, M. ve Taskin, V., Free vibration analysis of functionally graded beams with simply supported edges, Materials & Design, 28,5, 1651-1656, 2007.
- Sina, S. A., Navazi, H. M. ve Haddadpour, H., An analytical method for free vibration analysis of functionally graded beams, Materials & Design, 30,3, 741-747, 2009.
- Pradhan, K. K. ve Chakraverty, S., Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method, Composites Part B: Engineering, 51, 175-184, 2013.
- Öktem, A. S., Fonksiyonel derecelendirilmiş (FD) ileri kompozit plakların statik analizi, Journal of the Faculty of Engineering and Architecture of Gazi University, 29, 111-119, 2014.
- Nguyen, T.-K. ve Nguyen, B.-D., A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams, Journal of Sandwich Structures & Materials, 17,6, 613-631, 2015.
- Chen, W. R. ve Chang, H., Closed-form solutions for free vibration frequencies of functionally graded Euler-Bernoulli beams, Mechanics of Composite Materials, 53,1, 79-98, 2017.
- Lee, J. W. ve Lee, J. Y., Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122, 1-17, 2017.
- Turan M., Tabakalı kirişlerin static, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli, Doktora Tezi, Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon, 2018.
- Sayyad, A.S. ve Ghugal, Y.M., Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams, Asian Journal of Civil Engineering, 19, 607-623, 2018.
- Sayyad, A.S. ve Avhad, P.V., On static bending, elastic buckling and free vibration analysis of symmetric functionally graded sandwich beams, Journal of Solid Mechanics, 11, 166-180, 2019.
- Lee, J. W. ve Lee, J. Y., Contribution rates of normal and shear strain energies to the natural frequencies of functionally graded shear deformation beams, Composites Part B: Engineering, 159, 86-104, 2019.
There are 19 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | March 5, 2021 |
| Submission Date | August 1, 2019 |
| Acceptance Date | October 14, 2020 |
| Published in Issue | Year 2021 Volume: 36 Issue: 2 |