Araştırma Makalesi
BibTex RIS Kaynak Göster

Damped and Undamped Forced Vibration Analysis of Beams Made of Functionally Graded Materials

Yıl 2020, Cilt: 35 Sayı: 2, 497 - 510, 30.06.2020
https://doi.org/10.21605/cukurovaummfd.792455

Öz

In this study, a research has been conducted on the forced vibration behavior of beams with functionally graded (FG) material along the height of the cross-section under various dynamic loads. The effects of different boundary conditions, length-height (L/h) ratios and material variation coefficients on damped and undamped forced vibrations of Euler-Bernoulli and Timoshenko beams are also examined parametrically. The equations of motion which govern the behavior of the beams with FG material have been obtained with the help of the minimum total energy principle. The canonical differential equations obtained are solved numerically in the Laplace space with the aid of Complementary Functions Method (CFM). Kelvin type damping model is used in case of viscoelastic material. In this model, elastic constants are replaced by their complex counterparts in the Laplace space by means of the elastic- viscoelastic analogy. The accuracy of the results of the proposed method has been confirmed by comparing it with the results of the ANSYS finite element package program.

Kaynakça

  • 1. Qian, L.F., Ching, K.H., 2004. Static and Dynamic Analysis of 2-D Functionally Graded Elasticity by Using Meshless Local Petrov- Galerkin Method. Journal of the Chinese Institute of Engineers, 27(4), 491-503.
  • 2. Aydoğdu, M., Taşkın, V., 2007. Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges. Materials & Design, 28(5), 1651-1656.
  • 3. Li, X.F., 2008. A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler– bernoulli Beams. Journal of Sound and Vibrations, 318, 1210–1229.
  • 4. Sina, S.A., Navazi, H.M., Haddadpour, H., 2009. An Analytical Method for Free Vibration Analysis of Functionally Graded Beams. Materials and Design, 30, 741-747.
  • 5. Civalek, Ö., Kiracioglu, O., 2010. Free Vibration Analysis of Timoshenko Beams by DSC Method. Int. J. Numer. Meth. Biomed. Engng., 26, 1890-1898.
  • 6. Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F., 2011. Free Vibration Characteristics of a Functionally Graded Beam by Finite Element Method. Applied Mathematical Modelling, 35, 412-425.
  • 7. Atmane, H.A., Tounsi, A., Meftah, S.A., Belhadj, H.A., 2011. Free Vibration Behavior of Exponential Functionally Graded Beams with Varying Cross-section. Journal of Vibration and Control, 17(2), 311–318.
  • 8. Anandrao, K.S., Gupta, R.K., Ramachandran, P., Rao, G.V., 2012. Free Vibration Analysis of Functionally Graded Beams. Defence Science Journal, 62(3), 139-146.
  • 9. Pradhan, K.K., Chakraverty, S., 2013. Free Vibration of Euler and Timoshenko Functionally Graded Beams by Rayleigh–ritz Method. Composites: Part B, 51, 175–184.
  • 10. Demir, C., Öz, F.E., 2013. Free Vibration Analysis of a Functionally Graded Viscoelastic Supported Beam. Journal of Vibration and Control. DOI: 10.1177/1077546313479634.
  • 11. Su, H., Banerjee, J.R., 2015. Development of Dynamic Stiffness Method for Free Vibration of Functionally Graded Timoshenko Beams. Computers and Structures 147, 107–116.
  • 12. Jing, L.L., Ming, P.J., Zhang, W.P., Fu, L.R., Cao, Y.P., 2016. Static and Free Vibration Analysis of Functionally Graded Beams by Combination Timoshenko Theory and Finite Volume Method. Composite Structures, 138, 192-213.
  • 13. Avcar, M., Alwan, H.H.A., 2017. Free Vibration of Functionally Graded Rayleigh Beam. International Journal of Engineering & Applied Sciences (IJEAS), 9(2), 127-137.
  • 14. Lee, J.W., Lee, J.Y., 2017. Free Vibration Analysis of Functionally Graded Bernoulli- Euler Beams Using an Exact Transfer Matrix Expression. International Journal of Mechanical Sciences, 122, 1-17.
  • 15. Turan, M., Kahya, V., 2018. Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119-130, DOI: 10.31466/kfbd.453833.
  • 16. Akbaş, Ş.D., 2018. Fonksiyonel Derecelendirilmiş Ortotropik Bir Kirişin Statik ve Titreşim Davranışlarının İncelenmesi, BAUN Fen Bil. Enst. Dergisi, 20(1), 69-82.
  • 17. Nam, V.H., Vinh, P.V., Nguyen Van Chinh, N.V., Thom, D.V., Hong, T.T., 2019. A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory. Materials, doi: 10.3390/ma12030404.
  • 18. Noori, A.R., Aslan, T.A., Temel, B., 2020. Static Analysis of FG Beams via Complemantary Functions Method. European Mechanical Science, 4(1), 1-6.
  • 19. Yıldırım, S., Tütüncü, N., 2018. On the Inertio- Elastic Instability of Variable-thickness Functionally-graded Disks. Mechanics Research Communications, 91, 1–6.
  • 20. Yıldırım, S., Tütüncü, N., 2019. Effect of Magneto-Thermal Loads on the Rotational Instability of Heterogeneous Rotors. AIAA Journal, 57 (5) 2069-2074.
  • 21. Yontar, O., Aydın K., Keleş, İ., 2020. Practical Jointed Approach to Thermal Performance of Functionally Graded Material Annular Fin. Journal of Thermophysıcs and Heat Transfer, 34(1), 144-149.
  • 22. Çelebi, K, Yarımpabuç, D., Tütüncü, N., 2018. Free Vibration Analysis of Functionally Graded Beams Using Complementary Functions Method. Archive of Applied Mechanics, 88, 729–739.
  • 23. Temo, A., Yarımpabuç, D., 2019. The Effect of Uniform Magnetic Field on Pressurized FG Cylindrical and Spherical Vessels. European Mechanical Science, 3(4), 133-141.
  • 24. Çalım, F.F., 2020. Vibration Analysis of F unctionally Graded Timoshenko Beams on W inkler–pasternak Elastic Foundation. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44, 901-920.
  • 25. Çalım, F.F., 2016. Transient Analysis of Axially Functionally Graded Timoshenko Beams with Variable Cross-section. Composite Part B: Engineering, 98, 472-483.
  • 26. Aslan, T.A., Noori, A.R., Temel B., 2019. Birinci Mertebe Kayma Deformasyon Teorisine Dayalı FD Düz Eksenli Kirişlerin Serbest Titreşim Analizi. Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 34(4), 21-28.
  • 27. Aslan, T.A., Noori, A.R., Temel, B., 2019. Çift Yönlü Fonksiyonel Derecelenmiş Malzemeli Tımoshenko Kirişlerinin Serbest Titreşim Analizi. Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 8(3), 30-36.
  • 28. Temel B., Noori, A.R., 2020. A Unified Solution for the Vibration Analysis of Two- directional Functionally Graded Axisymmetric Mindlin–Reissner Plates with Variable Thickness. International Journal of Mechanical Sciences, 174, 1-20.
  • 29. Boley, B.A., Weiner, J.H., 1960. Theory of Thermal Stresses, John Wiley and Sons, New York.
  • 30. Aslan, T.A., Noori, A.R., Temel, B., 2018 Dikdörtgen Kesitli Viskoelastik Sikloid Çubukların Zorlanmış Titreşimi, Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 33(1), 151-162.
  • 31. Temel, B., Çalım, F.F., Tütüncü, N., 2004. Quasi-Static and Dynamic Response of Viscoelastic Helical Rods. Journal of Sound and Vibration, 271, 921-935.
  • 32. Durbin, F., 1974. Numerical Inversion of Laplace Transforms: an Efficient Improvement to Dubner and Abate’s Method. Computer Journal, 17, 371-376.
  • 33. Temel, B., 2004. Transient Analysis of Viscoelastic Helical Rods Subject to Time- Dependent Loads. International Journal of Solids and Structures, 41, 1605-1624.
  • 34. ANSYS, 2013. Inc Release 15.0, Canonsburg, PA.
  • 35. Spiegel, M.R., 1965. Laplace Transforms, McGraw-Hill New York.

Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi

Yıl 2020, Cilt: 35 Sayı: 2, 497 - 510, 30.06.2020
https://doi.org/10.21605/cukurovaummfd.792455

Öz

Bu çalışmada, kesit yüksekliği boyunca fonksiyonel olarak derecelendirilmiş (FD) malzemeli kirişlerin çeşitli dinamik yükler altında zorlanmış titreşim davranışı üzerine bir araştırma yapılmıştır. Farklı sınır koşulları, uzunluk-yükseklik (L/h) oranları ve malzeme değişim katsayılarının Euler-Bernoulli ve Timoshenko kirişlerinin sönümlü ve sönümsüz zorlanmış titreşimleri üzerindeki etkileri de parametrik olarak incelenmiştir. FD malzemeli çubukların davranışını idare eden hareket denklemleri, minimum toplam enerji prensibi yardımıyla elde edilmiştir. Elde edilen kanonik diferansiyel denklemler, Tamamlayıcı Fonksiyonlar Yöntemi (TFY) yardımıyla Laplace uzayında sayısal olarak çözülmüştür. Viskoelastik malzeme durumunda Kelvin tipi sönüm modeli kullanmıştır. Bu modelde elastik sabitler, elastik-viskoelastik analoji ile Laplace uzayındaki kompleks karşıtları ile değiştirilir. Önerilen yöntemin sonuçlarının doğruluğu, ANSYS sonlu elemanlar paket programının sonuçları ile karşılaştırılarak kanıtlanmıştır.

Kaynakça

  • 1. Qian, L.F., Ching, K.H., 2004. Static and Dynamic Analysis of 2-D Functionally Graded Elasticity by Using Meshless Local Petrov- Galerkin Method. Journal of the Chinese Institute of Engineers, 27(4), 491-503.
  • 2. Aydoğdu, M., Taşkın, V., 2007. Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges. Materials & Design, 28(5), 1651-1656.
  • 3. Li, X.F., 2008. A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler– bernoulli Beams. Journal of Sound and Vibrations, 318, 1210–1229.
  • 4. Sina, S.A., Navazi, H.M., Haddadpour, H., 2009. An Analytical Method for Free Vibration Analysis of Functionally Graded Beams. Materials and Design, 30, 741-747.
  • 5. Civalek, Ö., Kiracioglu, O., 2010. Free Vibration Analysis of Timoshenko Beams by DSC Method. Int. J. Numer. Meth. Biomed. Engng., 26, 1890-1898.
  • 6. Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F., 2011. Free Vibration Characteristics of a Functionally Graded Beam by Finite Element Method. Applied Mathematical Modelling, 35, 412-425.
  • 7. Atmane, H.A., Tounsi, A., Meftah, S.A., Belhadj, H.A., 2011. Free Vibration Behavior of Exponential Functionally Graded Beams with Varying Cross-section. Journal of Vibration and Control, 17(2), 311–318.
  • 8. Anandrao, K.S., Gupta, R.K., Ramachandran, P., Rao, G.V., 2012. Free Vibration Analysis of Functionally Graded Beams. Defence Science Journal, 62(3), 139-146.
  • 9. Pradhan, K.K., Chakraverty, S., 2013. Free Vibration of Euler and Timoshenko Functionally Graded Beams by Rayleigh–ritz Method. Composites: Part B, 51, 175–184.
  • 10. Demir, C., Öz, F.E., 2013. Free Vibration Analysis of a Functionally Graded Viscoelastic Supported Beam. Journal of Vibration and Control. DOI: 10.1177/1077546313479634.
  • 11. Su, H., Banerjee, J.R., 2015. Development of Dynamic Stiffness Method for Free Vibration of Functionally Graded Timoshenko Beams. Computers and Structures 147, 107–116.
  • 12. Jing, L.L., Ming, P.J., Zhang, W.P., Fu, L.R., Cao, Y.P., 2016. Static and Free Vibration Analysis of Functionally Graded Beams by Combination Timoshenko Theory and Finite Volume Method. Composite Structures, 138, 192-213.
  • 13. Avcar, M., Alwan, H.H.A., 2017. Free Vibration of Functionally Graded Rayleigh Beam. International Journal of Engineering & Applied Sciences (IJEAS), 9(2), 127-137.
  • 14. Lee, J.W., Lee, J.Y., 2017. Free Vibration Analysis of Functionally Graded Bernoulli- Euler Beams Using an Exact Transfer Matrix Expression. International Journal of Mechanical Sciences, 122, 1-17.
  • 15. Turan, M., Kahya, V., 2018. Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119-130, DOI: 10.31466/kfbd.453833.
  • 16. Akbaş, Ş.D., 2018. Fonksiyonel Derecelendirilmiş Ortotropik Bir Kirişin Statik ve Titreşim Davranışlarının İncelenmesi, BAUN Fen Bil. Enst. Dergisi, 20(1), 69-82.
  • 17. Nam, V.H., Vinh, P.V., Nguyen Van Chinh, N.V., Thom, D.V., Hong, T.T., 2019. A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory. Materials, doi: 10.3390/ma12030404.
  • 18. Noori, A.R., Aslan, T.A., Temel, B., 2020. Static Analysis of FG Beams via Complemantary Functions Method. European Mechanical Science, 4(1), 1-6.
  • 19. Yıldırım, S., Tütüncü, N., 2018. On the Inertio- Elastic Instability of Variable-thickness Functionally-graded Disks. Mechanics Research Communications, 91, 1–6.
  • 20. Yıldırım, S., Tütüncü, N., 2019. Effect of Magneto-Thermal Loads on the Rotational Instability of Heterogeneous Rotors. AIAA Journal, 57 (5) 2069-2074.
  • 21. Yontar, O., Aydın K., Keleş, İ., 2020. Practical Jointed Approach to Thermal Performance of Functionally Graded Material Annular Fin. Journal of Thermophysıcs and Heat Transfer, 34(1), 144-149.
  • 22. Çelebi, K, Yarımpabuç, D., Tütüncü, N., 2018. Free Vibration Analysis of Functionally Graded Beams Using Complementary Functions Method. Archive of Applied Mechanics, 88, 729–739.
  • 23. Temo, A., Yarımpabuç, D., 2019. The Effect of Uniform Magnetic Field on Pressurized FG Cylindrical and Spherical Vessels. European Mechanical Science, 3(4), 133-141.
  • 24. Çalım, F.F., 2020. Vibration Analysis of F unctionally Graded Timoshenko Beams on W inkler–pasternak Elastic Foundation. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44, 901-920.
  • 25. Çalım, F.F., 2016. Transient Analysis of Axially Functionally Graded Timoshenko Beams with Variable Cross-section. Composite Part B: Engineering, 98, 472-483.
  • 26. Aslan, T.A., Noori, A.R., Temel B., 2019. Birinci Mertebe Kayma Deformasyon Teorisine Dayalı FD Düz Eksenli Kirişlerin Serbest Titreşim Analizi. Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 34(4), 21-28.
  • 27. Aslan, T.A., Noori, A.R., Temel, B., 2019. Çift Yönlü Fonksiyonel Derecelenmiş Malzemeli Tımoshenko Kirişlerinin Serbest Titreşim Analizi. Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 8(3), 30-36.
  • 28. Temel B., Noori, A.R., 2020. A Unified Solution for the Vibration Analysis of Two- directional Functionally Graded Axisymmetric Mindlin–Reissner Plates with Variable Thickness. International Journal of Mechanical Sciences, 174, 1-20.
  • 29. Boley, B.A., Weiner, J.H., 1960. Theory of Thermal Stresses, John Wiley and Sons, New York.
  • 30. Aslan, T.A., Noori, A.R., Temel, B., 2018 Dikdörtgen Kesitli Viskoelastik Sikloid Çubukların Zorlanmış Titreşimi, Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 33(1), 151-162.
  • 31. Temel, B., Çalım, F.F., Tütüncü, N., 2004. Quasi-Static and Dynamic Response of Viscoelastic Helical Rods. Journal of Sound and Vibration, 271, 921-935.
  • 32. Durbin, F., 1974. Numerical Inversion of Laplace Transforms: an Efficient Improvement to Dubner and Abate’s Method. Computer Journal, 17, 371-376.
  • 33. Temel, B., 2004. Transient Analysis of Viscoelastic Helical Rods Subject to Time- Dependent Loads. International Journal of Solids and Structures, 41, 1605-1624.
  • 34. ANSYS, 2013. Inc Release 15.0, Canonsburg, PA.
  • 35. Spiegel, M.R., 1965. Laplace Transforms, McGraw-Hill New York.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Timuçin Alp Aslan

Ahmad Reshad Noori

Beytullah Temel

Yayımlanma Tarihi 30 Haziran 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 35 Sayı: 2

Kaynak Göster

APA Aslan, T. A., Noori, A. R., & Temel, B. (2020). Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(2), 497-510. https://doi.org/10.21605/cukurovaummfd.792455
AMA Aslan TA, Noori AR, Temel B. Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi. cukurovaummfd. Haziran 2020;35(2):497-510. doi:10.21605/cukurovaummfd.792455
Chicago Aslan, Timuçin Alp, Ahmad Reshad Noori, ve Beytullah Temel. “Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü Ve Sönümsüz Zorlanmış Titreşim Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35, sy. 2 (Haziran 2020): 497-510. https://doi.org/10.21605/cukurovaummfd.792455.
EndNote Aslan TA, Noori AR, Temel B (01 Haziran 2020) Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35 2 497–510.
IEEE T. A. Aslan, A. R. Noori, ve B. Temel, “Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi”, cukurovaummfd, c. 35, sy. 2, ss. 497–510, 2020, doi: 10.21605/cukurovaummfd.792455.
ISNAD Aslan, Timuçin Alp vd. “Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü Ve Sönümsüz Zorlanmış Titreşim Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 35/2 (Haziran 2020), 497-510. https://doi.org/10.21605/cukurovaummfd.792455.
JAMA Aslan TA, Noori AR, Temel B. Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi. cukurovaummfd. 2020;35:497–510.
MLA Aslan, Timuçin Alp vd. “Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü Ve Sönümsüz Zorlanmış Titreşim Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, c. 35, sy. 2, 2020, ss. 497-10, doi:10.21605/cukurovaummfd.792455.
Vancouver Aslan TA, Noori AR, Temel B. Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi. cukurovaummfd. 2020;35(2):497-510.