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INVESTIGATION OF THE FREE VIBRATION OF AN ALUMINUM BEAM COATED WITH FGM CONTAINING POROSITIES

Year 2020, Volume: 9 Issue: 2, 1090 - 1099, 07.08.2020
https://doi.org/10.28948/ngumuh.658473

Abstract

In this study, the free vibration analysis of an aluminum beam coated with functionally graded material (FGM) containing porosities was investigated. The modulus of elasticity and density of the functionally graded material is assumed to vary with a polynomial function along the layer thickness of the beam. In order to represent the FGM in a realistic way, the coating thickness consists of 25 layers and each layer is modeled as homogeneous isotropic in itself. The effective density and modulus of elasticity of the FGM is determined using classical lamination theory. In this study, the solution of the problem was realized by using the finite element method using Timoshenko beam theory which includes first order shear deformation. The FEM code is written in MATLAB and the natural frequencies of the beam are calculated. A parametric study is conducted to show the influences of porosity (a), core thickness to FGM thickness ratio (h/H), beam span to height ratio (L/H) and power law index (n) on the natural beam frequencies. It was observed that the studied parameters had a significant effect on the natural frequencies.

References

  • E. Demir, “Vibration and damping behaviors of symmetric layered functional graded sandwich beams,” Struct Eng Mech, vol. 62(6), pp. 771-780, 2017.
  • S. Rajasekaran and H. B. Khaniki, “Free vibration analysis of bi-directional functionally graded single/multi-cracked beams,” Int Journal of Mech Sci, vol. 144, pp. 341–356, 2018.
  • Z. Wang, X. Wang, G. Xu, S. Cheng and T. Zeng “ Free vibration of two-directional functionally graded beams,” Composite Structures, vol. 135, pp. 191–198, 2016.
  • 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(3), pp. 792-806, 2017.
  • C. Mohcine, M. El Bekkaye and K. El Bikri, “Geometrically Non-Linear Free and Forced Vibration of Clamped- Clamped Functionally Graded Beam with Discontinuities,” Procedia Engineering, vol. 199, pp. 1870–1875, 2017.
  • K. Bouakkaz, L. Hadji, N. Zouatnia and E. A. Adda Bedia, “An analytical method for free vibration analysis of functionally graded sandwich beams,” Wind and Structures, vol. 23(1), pp. 59-73, 2016.
  • Z. Su, G. Jin, Y. Wang and X. Ye, “A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations,” Acta Mech, vol. 227, pp. 1493–1514, 2016.
  • M. Soltanpour, M. Ghadiri, A. Yazdi and M. Safi, “Free transverse vibration analysis of size dependent Timoshenko FG cracked nanobeams resting on elastic medium,” Microsyst Technol, vol. 23, pp. 1813–1830, 2017.
  • S. D. Akbaş, "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory," Int Journal of Str Stab and Dynamics, vol. 16(10), 1750033, 2016.
  • T. Van Lien, N. T. Duc, and N.T. Khiem, “Free vibration analysis of multiple cracked functionally graded timoshenko beams,” Lat Am Journal of Solids and Structures, vol. 14, pp. 1752-1766, 2017.
  • S.Shabani, Y.Cunedioglu, “Free vibration analysis of cracked functionally graded non-uniform beams,” Materials Research Express, Vol. 17(1), pp 1-15, 2020.
  • H. Çallıoğlu, E. Demir, Y. Yılmaz and M. Sayer, “Vibration analysis of functionally graded sandwich beam with variable cross-section,” Mathematical and Computational Applications, vol. 18(3), pp. 351-360, 2013.
  • D. L. Logan, A First Course in the Finite Element Method, Boston: Cengage Learning, 2015.
  • M. Petyt, Introduction to Finite Element Vibration Analysis, New York: Cambridge, 2010.
  • E.F.Erdurcan, Y.Cunedioglu, “Free Vibration Analysis of a Functionally Graded Material Coated Aluminum Beam,” AIAA Journal, vol. 58(2), 2020.
  • R.F. Gibson, Principles of Composite Materials, Boca Raton: CRC Press, 2016.

POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ

Year 2020, Volume: 9 Issue: 2, 1090 - 1099, 07.08.2020
https://doi.org/10.28948/ngumuh.658473

Abstract

Bu çalışmada çekirdek tabakası alüminyum ve yüzeyleri porosite ihtiva eden fonksiyonel derecelendirilmiş malzeme (FDM) ile kaplı simetrik yapıda ankastre sandviç bir kirişin serbest titreşim analizi incelenmiştir. Fonksiyonel derecelendirilmiş malzemenin elastisite modülü ve yoğunluğu kirişin tabaka kalınlığı boyunca bir polinom fonksiyonla değiştiği kabul edilmiştir. FDM’yi gerçeğe yakın bir şekilde temsil etmek için kaplama kalınlığının 25 tabakadan oluştuğu ve her bir tabaka kendi içinde homojen izotrop olarak modellenmiştir. Bu yapılara ait efektif yoğunluk ve elastisite modülü tabakalı kompozit kiriş teorisi kullanılarak belirlenmiştir. Çalışmada birinci mertebe kayma deformasyonu içeren Timoshenko kiriş teorisi kullanılarak problemin çözümü sonlu elemanlar metoduyla gerçekleştirilmiştir. Kirişin doğal frekanslarının hesaplanması için MATLAB’ta sonlu elemanlar kodu yazılmıştır. Çalışmada porosite hacim oranının (a), çekirdek tabaka kalınlığının FDM kalınlık oranına (h/H), kiriş açıklığının yüksekliğine oranının (L/H) ve FDM’nin mekanik özelliklerini belirleyen polinom parametresinin (n) doğal frekansların üzerindeki etkisi incelenmiştir. İncelenen parametrelerin kirişin doğal frekanslarını önemli ölçüde etkilediği gözlemlenmiştir.

References

  • E. Demir, “Vibration and damping behaviors of symmetric layered functional graded sandwich beams,” Struct Eng Mech, vol. 62(6), pp. 771-780, 2017.
  • S. Rajasekaran and H. B. Khaniki, “Free vibration analysis of bi-directional functionally graded single/multi-cracked beams,” Int Journal of Mech Sci, vol. 144, pp. 341–356, 2018.
  • Z. Wang, X. Wang, G. Xu, S. Cheng and T. Zeng “ Free vibration of two-directional functionally graded beams,” Composite Structures, vol. 135, pp. 191–198, 2016.
  • 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(3), pp. 792-806, 2017.
  • C. Mohcine, M. El Bekkaye and K. El Bikri, “Geometrically Non-Linear Free and Forced Vibration of Clamped- Clamped Functionally Graded Beam with Discontinuities,” Procedia Engineering, vol. 199, pp. 1870–1875, 2017.
  • K. Bouakkaz, L. Hadji, N. Zouatnia and E. A. Adda Bedia, “An analytical method for free vibration analysis of functionally graded sandwich beams,” Wind and Structures, vol. 23(1), pp. 59-73, 2016.
  • Z. Su, G. Jin, Y. Wang and X. Ye, “A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations,” Acta Mech, vol. 227, pp. 1493–1514, 2016.
  • M. Soltanpour, M. Ghadiri, A. Yazdi and M. Safi, “Free transverse vibration analysis of size dependent Timoshenko FG cracked nanobeams resting on elastic medium,” Microsyst Technol, vol. 23, pp. 1813–1830, 2017.
  • S. D. Akbaş, "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory," Int Journal of Str Stab and Dynamics, vol. 16(10), 1750033, 2016.
  • T. Van Lien, N. T. Duc, and N.T. Khiem, “Free vibration analysis of multiple cracked functionally graded timoshenko beams,” Lat Am Journal of Solids and Structures, vol. 14, pp. 1752-1766, 2017.
  • S.Shabani, Y.Cunedioglu, “Free vibration analysis of cracked functionally graded non-uniform beams,” Materials Research Express, Vol. 17(1), pp 1-15, 2020.
  • H. Çallıoğlu, E. Demir, Y. Yılmaz and M. Sayer, “Vibration analysis of functionally graded sandwich beam with variable cross-section,” Mathematical and Computational Applications, vol. 18(3), pp. 351-360, 2013.
  • D. L. Logan, A First Course in the Finite Element Method, Boston: Cengage Learning, 2015.
  • M. Petyt, Introduction to Finite Element Vibration Analysis, New York: Cambridge, 2010.
  • E.F.Erdurcan, Y.Cunedioglu, “Free Vibration Analysis of a Functionally Graded Material Coated Aluminum Beam,” AIAA Journal, vol. 58(2), 2020.
  • R.F. Gibson, Principles of Composite Materials, Boca Raton: CRC Press, 2016.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Mechanical Engineering, Material Production Technologies
Journal Section Mechanical Engineering
Authors

Ersoy Fatih Erdurcan 0000-0001-6758-7350

Yusuf Cunedioğlu 0000-0002-3424-0454

Publication Date August 7, 2020
Submission Date December 12, 2019
Acceptance Date August 5, 2020
Published in Issue Year 2020 Volume: 9 Issue: 2

Cite

APA Erdurcan, E. F., & Cunedioğlu, Y. (2020). POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 9(2), 1090-1099. https://doi.org/10.28948/ngumuh.658473
AMA Erdurcan EF, Cunedioğlu Y. POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ. NOHU J. Eng. Sci. August 2020;9(2):1090-1099. doi:10.28948/ngumuh.658473
Chicago Erdurcan, Ersoy Fatih, and Yusuf Cunedioğlu. “POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9, no. 2 (August 2020): 1090-99. https://doi.org/10.28948/ngumuh.658473.
EndNote Erdurcan EF, Cunedioğlu Y (August 1, 2020) POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9 2 1090–1099.
IEEE E. F. Erdurcan and Y. Cunedioğlu, “POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ”, NOHU J. Eng. Sci., vol. 9, no. 2, pp. 1090–1099, 2020, doi: 10.28948/ngumuh.658473.
ISNAD Erdurcan, Ersoy Fatih - Cunedioğlu, Yusuf. “POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9/2 (August 2020), 1090-1099. https://doi.org/10.28948/ngumuh.658473.
JAMA Erdurcan EF, Cunedioğlu Y. POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ. NOHU J. Eng. Sci. 2020;9:1090–1099.
MLA Erdurcan, Ersoy Fatih and Yusuf Cunedioğlu. “POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 9, no. 2, 2020, pp. 1090-9, doi:10.28948/ngumuh.658473.
Vancouver Erdurcan EF, Cunedioğlu Y. POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ. NOHU J. Eng. Sci. 2020;9(2):1090-9.

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