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Transfer Matris Metodu ile Fonksiyonel Derecelendirilmiş Sandviç Kirişlerin Titreşim Analizi

Year 2020, Volume: 11 Issue: 1, 259 - 269, 27.03.2020
https://doi.org/10.24012/dumf.664735

Abstract

Fonksiyonel derecelendirilmiş malzemeler geleneksel malzemelerin uygun olmadığı çalışma koşulları için tasarlanmış özel bir kompozit malzeme sınıfıdır. Malzeme özellikleri istenen doğrultuda bir fonksiyona bağlı olarak değişmektedir. Malzeme özelliklerinde keskin geçişler olmaması nedeniyle katmanlı kompozit yapılarda karşılaşılan problemleri ortadan kaldıran fonksiyonel derecelendirilmiş malzemeler sandviç yapılar içinde öz veya yüzey tabakası olarak kullanılabilmektedir. Bu çalışmada fonksiyonel derecelendirilmiş sandviç kirişlerin titreşim analizi yapılmıştır. Sandviç kirişin yüzey tabakaları fonksiyonel derecelendirilmiş, öz tabakası izotropik malzeme olarak kabul edilmiştir. Sandviç kirişin yer değiştirme bileşenleri Euler-Bernoulli kiriş teorisi ile tanımlanmış, farklı sınır koşulları için elde edilen kiriş denklemi transfer matris metodu ile çözülmüştür. Sandviç öz ve yüzey tabakası kalınlık oranlarının ve hacimsel değişim üstelinin değişiminin doğal frekansın değişimi üzerindeki etkileri incelenmiştir. Sandviç öz ve yüzey tabakası kalınlık oranlarının doğal frekans değeri üzerinde etkin olduğu ve hacimsel değişim üstelindeki artışın tüm sınır koşulları için boyutsuz doğal frekans değerini düşürdüğü görülmüştür

References

  • [1] T.K. Nguyen and B.D. Nguyen, “New higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams,”, Journal of Sandwich Structures and Materials, vol. 17, no 6, pp. 613–63, 2015. https://doi.org/10.1177/1099636215589237
  • [2] Pınar Aydan Demirhan, “Fonksiyonel Derecelendirilmiş Sandviç Kiriş Ve Plakların Dört Değişkenli Kayma Deformasyon Teorisi İle Eğilme Ve Titreşim Analizi”, Doktora Tezi, Trakya Üniversitesi Fen Bilimleri Enstitüsü, Edirne, 2016.
  • [3] X.F. Li, “A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams,”, Journal of Sound and Vibration, vol. 318, pp. 1210–1229, 2008. https://doi.org/10.1016/j.jsv.2008.04.056
  • [4] S.A. Sina, H.M. Navazi and H. Haddadpour, “An analytical method for free vibration analysis of functionally graded beams,”, Materials and Design, vol. 30, pp. 741–747, 2009. https://doi.org/10.1016/j.matdes.2008.05.015
  • [5] T.P. Vo, H.T. Thai, T.K. Nguyen, A. Maheri and J. Lee, “Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory,”, Engineering Structures, vol. 64, pp. 12–22, 2014. http://dx.doi.org/10.1016/j.engstruct.2014.01.029
  • [6] T.P. Vo, H.T. Thai, T.K. Nguyen, F. Inam and J. Lee, “A quasi-3D theory for vibration and buckling of functionally graded sandwich beams,”, Composite Structures, vol. 119, pp. 1–12, 2015. http://dx.doi.org/10.1016/j.compstruct.2014.08.006
  • [7] N. Wattanasakulpong and V. Ungbhakorn, “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities,”, Aerospace Science and Technology, vol. 32, pp. 111–120, 2014. http://dx.doi.org/10.1016/j.ast.2013.12.002
  • [8] N. Wattanasakulpong and A. Chaikittiratana, “Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method,”, Meccanica, vol. 50, pp.1331–1342, 2015. http://dx.doi.org/10.1007/s11012-014-0094-8
  • [9] T.K. Nguyen, T.T.P. Nguyen, T.P. Vo and H.T. Thai, “Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory,”, Composites Part B, vol. 76, pp. 273-285, 2015. http://dx.doi.org/10.1016/j.compositesb.2015.02.032
  • [10] T.K. Nguyen, T.P. Vo, B.D. Nguyen and J. Lee, “An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory,”, Composite Structures, vol. 156, 238–252, 2016. http://dx.doi.org/10.1016/j.compstruct.2015.11.074
  • [11] A.I. Osofero, T.P. Vo, T.K. Nguyen and J. Lee, “Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories,”, Journal of Sandwich Structures and Materials, Vol. 18, no 1, pp. 3–29, 2018. http://dx.doi.org/10.1177/1099636215582217
  • [12] S. Kitipornchai, D. Chen and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets,”, Materials and Design vol. 116, pp. 656–665, 2017. http://dx.doi.org/10.1016/j.matdes.2016.12.061
  • [13] M. Boiangiu, V. Ceausu, C.D. Untaroiu, “A transfer matrix method for free vibration analysis of Euler-Bernoulli beams with variable cross section,”, Journal of Vibration and Control, vol.22, no.11, pp. 2591-2602, 2014. https://doi.org/10.1177/1077546314550699
  • [14] L.C. Trinh, T.P. Vo, A.I. Osofero and J. Lee, “Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach,”, Composite Structures, vol. 156, pp. 263–275, 2016. http://dx.doi.org/10.1016/j.compstruct.2015.11.010
  • [15] P.A. Demirhan and V. Taskin, “Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory,”, Composite Structures, vol. 177, pp. 80–95, 2017. http://dx.doi.org/10.1016/j.compstruct.2017.06.048
  • [16] P.A. Demirhan and V. Taskin, “Static analysis of simply supported functionally graded sandwich plates by using four variable plate theory,”, Teknik Dergi, vol. 30, no 2, pp. 8987-9007, 2019a. https://dx.doi.org/10.18400/tekderg.396672
  • [17] P.A. Demirhan and V. Taskin, “Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach,”, Composites Part B, vol. 160, pp. 661–676, 2019b. https://doi.org/10.1016/j.compositesb.2018.12.020
  • [18] X. Li, L. Li, Y. Hu, Z. Ding and W. Deng, “Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory,”, Composite Structures, vol. 165, pp. 250–265, 2017. http://dx.doi.org/10.1016/j.compstruct.2017.01.032
  • [19] Y.S. Al Rjoub and A.G. Hamad, “Free vibration of functionally euler-bernoulli and timoshenko graded porous beams using the transfer matrix method,”, KSCE Journal of Civil Engineering, vol. 21, no 3, pp.792-806, 2017. https://doi.org/10.1007/s12205-016-0149-6
  • [20] V. Kahya and M. Turan, “Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element,”, Composites Part B, vol. 146, pp.198–212, 2018. https://doi.org/10.1016/j.compositesb.2018.04.011
  • [21] M. Şen, M. Hüseyinoğlu, “Investigation of the Effects of Polyurethane Foam Reinforcement Thickness on Modal Properties of Sandwich Beams”, Muş Alparslan Üniversitesi Fen Bilimleri Dergisi,vol. 6, no.1, pp. 511-517, 2018. https://dergipark.org.tr/tr/pub/msufbd/issue/37908/438101
  • [22] M. Hüseyinoglu, T. Abut, “İki Ucu Ankastre U Çerçeve Yapının Modal Analizi”, Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, vol. 7, pp.657-665, 2019. https://doi.org/10.18586/msufbd.637678.
  • [23] M. Hüseyinoğlu, M. Şen, O. Yiğid, O. Çakar, “Dynamic Analysis of Uniform and Non-Uniform Cross-Section Cantilever Sandwich Beams”, European Journal of Technique (EJT), vol. 9, no.2, pp. 286-297, 2019. https://doi.org/10.36222/ejt.632784
Year 2020, Volume: 11 Issue: 1, 259 - 269, 27.03.2020
https://doi.org/10.24012/dumf.664735

Abstract

References

  • [1] T.K. Nguyen and B.D. Nguyen, “New higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams,”, Journal of Sandwich Structures and Materials, vol. 17, no 6, pp. 613–63, 2015. https://doi.org/10.1177/1099636215589237
  • [2] Pınar Aydan Demirhan, “Fonksiyonel Derecelendirilmiş Sandviç Kiriş Ve Plakların Dört Değişkenli Kayma Deformasyon Teorisi İle Eğilme Ve Titreşim Analizi”, Doktora Tezi, Trakya Üniversitesi Fen Bilimleri Enstitüsü, Edirne, 2016.
  • [3] X.F. Li, “A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams,”, Journal of Sound and Vibration, vol. 318, pp. 1210–1229, 2008. https://doi.org/10.1016/j.jsv.2008.04.056
  • [4] S.A. Sina, H.M. Navazi and H. Haddadpour, “An analytical method for free vibration analysis of functionally graded beams,”, Materials and Design, vol. 30, pp. 741–747, 2009. https://doi.org/10.1016/j.matdes.2008.05.015
  • [5] T.P. Vo, H.T. Thai, T.K. Nguyen, A. Maheri and J. Lee, “Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory,”, Engineering Structures, vol. 64, pp. 12–22, 2014. http://dx.doi.org/10.1016/j.engstruct.2014.01.029
  • [6] T.P. Vo, H.T. Thai, T.K. Nguyen, F. Inam and J. Lee, “A quasi-3D theory for vibration and buckling of functionally graded sandwich beams,”, Composite Structures, vol. 119, pp. 1–12, 2015. http://dx.doi.org/10.1016/j.compstruct.2014.08.006
  • [7] N. Wattanasakulpong and V. Ungbhakorn, “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities,”, Aerospace Science and Technology, vol. 32, pp. 111–120, 2014. http://dx.doi.org/10.1016/j.ast.2013.12.002
  • [8] N. Wattanasakulpong and A. Chaikittiratana, “Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method,”, Meccanica, vol. 50, pp.1331–1342, 2015. http://dx.doi.org/10.1007/s11012-014-0094-8
  • [9] T.K. Nguyen, T.T.P. Nguyen, T.P. Vo and H.T. Thai, “Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory,”, Composites Part B, vol. 76, pp. 273-285, 2015. http://dx.doi.org/10.1016/j.compositesb.2015.02.032
  • [10] T.K. Nguyen, T.P. Vo, B.D. Nguyen and J. Lee, “An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory,”, Composite Structures, vol. 156, 238–252, 2016. http://dx.doi.org/10.1016/j.compstruct.2015.11.074
  • [11] A.I. Osofero, T.P. Vo, T.K. Nguyen and J. Lee, “Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories,”, Journal of Sandwich Structures and Materials, Vol. 18, no 1, pp. 3–29, 2018. http://dx.doi.org/10.1177/1099636215582217
  • [12] S. Kitipornchai, D. Chen and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets,”, Materials and Design vol. 116, pp. 656–665, 2017. http://dx.doi.org/10.1016/j.matdes.2016.12.061
  • [13] M. Boiangiu, V. Ceausu, C.D. Untaroiu, “A transfer matrix method for free vibration analysis of Euler-Bernoulli beams with variable cross section,”, Journal of Vibration and Control, vol.22, no.11, pp. 2591-2602, 2014. https://doi.org/10.1177/1077546314550699
  • [14] L.C. Trinh, T.P. Vo, A.I. Osofero and J. Lee, “Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach,”, Composite Structures, vol. 156, pp. 263–275, 2016. http://dx.doi.org/10.1016/j.compstruct.2015.11.010
  • [15] P.A. Demirhan and V. Taskin, “Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory,”, Composite Structures, vol. 177, pp. 80–95, 2017. http://dx.doi.org/10.1016/j.compstruct.2017.06.048
  • [16] P.A. Demirhan and V. Taskin, “Static analysis of simply supported functionally graded sandwich plates by using four variable plate theory,”, Teknik Dergi, vol. 30, no 2, pp. 8987-9007, 2019a. https://dx.doi.org/10.18400/tekderg.396672
  • [17] P.A. Demirhan and V. Taskin, “Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach,”, Composites Part B, vol. 160, pp. 661–676, 2019b. https://doi.org/10.1016/j.compositesb.2018.12.020
  • [18] X. Li, L. Li, Y. Hu, Z. Ding and W. Deng, “Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory,”, Composite Structures, vol. 165, pp. 250–265, 2017. http://dx.doi.org/10.1016/j.compstruct.2017.01.032
  • [19] Y.S. Al Rjoub and A.G. Hamad, “Free vibration of functionally euler-bernoulli and timoshenko graded porous beams using the transfer matrix method,”, KSCE Journal of Civil Engineering, vol. 21, no 3, pp.792-806, 2017. https://doi.org/10.1007/s12205-016-0149-6
  • [20] V. Kahya and M. Turan, “Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element,”, Composites Part B, vol. 146, pp.198–212, 2018. https://doi.org/10.1016/j.compositesb.2018.04.011
  • [21] M. Şen, M. Hüseyinoğlu, “Investigation of the Effects of Polyurethane Foam Reinforcement Thickness on Modal Properties of Sandwich Beams”, Muş Alparslan Üniversitesi Fen Bilimleri Dergisi,vol. 6, no.1, pp. 511-517, 2018. https://dergipark.org.tr/tr/pub/msufbd/issue/37908/438101
  • [22] M. Hüseyinoglu, T. Abut, “İki Ucu Ankastre U Çerçeve Yapının Modal Analizi”, Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, vol. 7, pp.657-665, 2019. https://doi.org/10.18586/msufbd.637678.
  • [23] M. Hüseyinoğlu, M. Şen, O. Yiğid, O. Çakar, “Dynamic Analysis of Uniform and Non-Uniform Cross-Section Cantilever Sandwich Beams”, European Journal of Technique (EJT), vol. 9, no.2, pp. 286-297, 2019. https://doi.org/10.36222/ejt.632784
There are 23 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Pınar Aydan Demirhan

Vedat Taşkın 0000-0002-3013-2317

Publication Date March 27, 2020
Submission Date December 25, 2019
Published in Issue Year 2020 Volume: 11 Issue: 1

Cite

IEEE P. A. Demirhan and V. Taşkın, “Transfer Matris Metodu ile Fonksiyonel Derecelendirilmiş Sandviç Kirişlerin Titreşim Analizi”, DUJE, vol. 11, no. 1, pp. 259–269, 2020, doi: 10.24012/dumf.664735.
DUJE tarafından yayınlanan tüm makaleler, Creative Commons Atıf 4.0 Uluslararası Lisansı ile lisanslanmıştır. Bu, orijinal eser ve kaynağın uygun şekilde belirtilmesi koşuluyla, herkesin eseri kopyalamasına, yeniden dağıtmasına, yeniden düzenlemesine, iletmesine ve uyarlamasına izin verir. 24456