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Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi

Year 2021, Volume: 10 Issue: 1, 319 - 327, 15.01.2021
https://doi.org/10.28948/ngumuh.823385

Abstract

Bu çalışmanın amacı, eksenel fonksiyonel derecelendirilmiş (EFD) kesin geometri tarifi üzerinden elde edilen dairesel olmayan (fıçı, hiperboloidal ve eliptik) helislerin doğal frekanslarını incelemektir. Timoshenko çubuk kuramı üstünden geliştirilen karışık sonlu eleman yönteminde kesit çarpılması da gözetilerek serbest titreşim analizi yapılmıştır. İki düğüm noktalı eğrisel sonlu elemanın her düğüm noktasındaki 12 değişken; üçü yer değiştirmeler, üçü kesit dönmeleri, üçü kuvvetler ikisi eğilme biri burulma momentleridir. Eksenel FD dairesel olmayan geometriye sahip ve kesin geometri üzerinden tariflenen helislerin serbest titreşim analizi farklı sınır koşulları ve malzeme gradyenti değişimleri üzerinden detaylıca tartışılmıştır. Yöntem literatür ya da ANSYS ile doğrulandıktan sonra literatür için tamamen özgün problemler çözülmüştür

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Free vibration analysis of axially functionally graded helices via mixed finite element method

Year 2021, Volume: 10 Issue: 1, 319 - 327, 15.01.2021
https://doi.org/10.28948/ngumuh.823385

Abstract

The objective of this study is to investigate the natural frequencies of axially functionally graded (AFG) non-circular (barrel, hyperboloidal and elliptical) helices based on exact geometry. Free vibration analysis is performed using the mixed finite element method based on Timoshenko beam theory by considering cross-sectional warping effect. A two-noded curved finite element involves 12 field variables at each node, three displacements, three cross-sectional rotations, three forces, and three moments. The free vibration analysis of axially FG exact non-circular helical geometries is discussed in detail over different boundary conditions and material gradient indexes. After verifying the algorithm with the problems available in the literature and ANSYS software, original problems for the literature are solved.

References

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  • S. R. Dhineshkumar, M. Duraiselvam, S. Natarajan, S. S. Panwar, T. Jena and M. A. Khan Enhancement of strain tolerance of functionally graded LaTi2Al9O19 thermal barrier coating through ultra-short pulse based laser texturing. Surface and Coatings Technology, 304, 263-271, 2016. https://doi.org/10.1016/j.surfcoat. 2016.07.018.
  • S. M. Naga, M. Awaad, H. F. El-Maghraby, A. M. Hassan, M. Elhoriny, A. Killinger and R. Gadow Effect of La2Zr2O7 coat on the hot corrosion of multi-layer thermal barrier coatings. Materials & Design, 102, 1-7, 2016. https://doi.org/10.1016/j.matdes.2016.03.133
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  • X.-F. Li, Y.-A. Kang and J.-X. Wu, Exact frequency equations of free vibration of exponentially functionally graded beams. Applied Acoustics, 74, 413–420, 2013. https://doi.org/10.1016/j.apacoust.20 12.08.003
  • S. Rajasekaran and E. N. Tochaei, Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order. Meccanica 49(4), 995–1009, 2014. https: //doi.org/10.1007/s11012-013-9847-z
  • K. Sarkar and R. Ganguli, Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed–fixed boundary condition. Composites Part B: Engineering, 58, 361–370, 2014. https://doi.org/10.1016/j.compositesb.20 13.10.077
  • F. F. Calim, Transient analysis of axially functionally graded Timoshenko beams with variable cross-section. Composites Part B: Engineering 98, 472–483, 2016. https://doi.org/10.1016/j.compositesb.2016.05.040
  • Y. Zhao, Y. Huang and M. Guo, A novel approach for free vibration of axially functionally graded beams with non-uniform cross-section based on Chebyshev polynomials theory. Composite Structures, 168, 277–284, 2017. https://doi.org/10.1016/j.compstruct.2017. 02.012
  • D. Cao, Y. Gao, M. Yao and W. Zhang, Free vibration of axially functionally graded beams using the asymptotic development method. Engineering Structures, 173, 442–448, 2018. https://doi.org/ 10.1016/j.engstruct.20 18.06.111
  • S. Šalinic, A. Obradovic and A. Tomovic, Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. Composites Part B: Engineering, 150, 135–143, 2018. https://doi.org/10.1016/j.compositesb. 2018.05.060
  • 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 165, 250–265, 2017. https://doi.org/10.1016/j.compstruct.2017.01.032
  • M. Sari, M. Shaat and A. Abdelkefi, Frequency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal residuals. Composite Structures, 163, 280–292, 2017. https://doi.org/10.10 16/j.compstruct.2016.11.093
  • M. H. Ghayesh and H. Farokhi, Mechanics of tapered axially functionally graded shallow arches. Composite Structures 188, 233–241, 2018. https://doi.org/10. 1016/ j.compstruct.2017.11.017
  • M. Chen, G. Jin, Y. Zhang, F. Niu and Z. Liu, Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thickness. Composite Structures, 207, 304–322, 2019. https://doi.org/10.1016/j.compstruct.2018.09.029
  • X. Zhang, Z. Ye and Y. Zhou, A Jacobi polynomial based approximation for free vibration analysis of axially functionally graded material beams. Composite Structures, 225, 111070, 2019. https://doi.org/10.1016/ j.compstruct.2019.111070
  • R. Talebitooti, S. O. Rezazadeh and A. Amiri, Comprehensive semi-analytical vibration analysis of rotating tapered AFG nanobeams based on nonlocal elasticity theory considering various boundary conditions via differential transformation method. Composites Part B: Engineering, 160, 412–435, 2019. https://doi.org/10.1016/j.compositesb.2018.12.085
  • S. Rajasekaran, Analysis of curved beams using a new differential transformation based curved beam element. Meccanica, 49, 863–886, 2014. https://doi.org/10.1007 /s11012-013-9835-3
  • G. C. Tsiatas and A. E. Charalampakis, Optimizing the natural frequencies of axially functionally graded beams and arches. Composite Structures, 160, 256–266, 2017. https://doi.org/10.1016/j.compstruct. 2016.10.057
  • J. K. Lee and B. K. Lee, In-plane free vibration of uniform circular arches made of axially functionally graded materials. International Journal of Structural Stability and Dynamics, 19, 1950084, 2019. https://doi.org/10. 1142/S0219455419500846
  • R. Noori, T. A. Aslan and B. Temel, An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with nonuniform cross section. Composite Structures, 200, 701-710, 2018. https://doi.org/10.1016/j.compstruct. 2018.05.07 7
  • B. Temel and A. R. Noori, Out-of-plane vibrations of shear-deformable AFG cycloidal beams with variable cross section. Applied Acoustics, 155, 84–96, 2019. https://doi.org/10.1016/j.apacoust.2019.05.010
  • F.F. Calim and Y.C. Cuma, Vibration analysis of nonuniform hyperboloidal and barrel helices made of functionally graded material. Mechanics Based Design of Structures and Machines, 2020. https://doi.org/ 10.1080/15397734.2020.1822181
  • K. Nagaya, S. Takeda and Y. Nakata, Free vibration of coil springs of arbitrary shape. International Journal for Numerical Methods in Engineering 23, 1081–1099, 1986. https://doi.org/10.1002/nme.1620230607
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There are 63 citations in total.

Details

Primary Language Turkish
Subjects Civil Engineering
Journal Section Civil Engineering
Authors

Merve Ermiş 0000-0003-0201-6586

Publication Date January 15, 2021
Submission Date November 9, 2020
Acceptance Date December 16, 2020
Published in Issue Year 2021 Volume: 10 Issue: 1

Cite

APA Ermiş, M. (2021). Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 10(1), 319-327. https://doi.org/10.28948/ngumuh.823385
AMA Ermiş M. Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. NOHU J. Eng. Sci. January 2021;10(1):319-327. doi:10.28948/ngumuh.823385
Chicago Ermiş, Merve. “Eksenel Fonksiyonel Derecelendirilmiş Helislerin karışık Sonlu Eleman yöntemi Ile Serbest titreşim Analizi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 10, no. 1 (January 2021): 319-27. https://doi.org/10.28948/ngumuh.823385.
EndNote Ermiş M (January 1, 2021) Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 10 1 319–327.
IEEE M. Ermiş, “Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi”, NOHU J. Eng. Sci., vol. 10, no. 1, pp. 319–327, 2021, doi: 10.28948/ngumuh.823385.
ISNAD Ermiş, Merve. “Eksenel Fonksiyonel Derecelendirilmiş Helislerin karışık Sonlu Eleman yöntemi Ile Serbest titreşim Analizi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 10/1 (January 2021), 319-327. https://doi.org/10.28948/ngumuh.823385.
JAMA Ermiş M. Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. NOHU J. Eng. Sci. 2021;10:319–327.
MLA Ermiş, Merve. “Eksenel Fonksiyonel Derecelendirilmiş Helislerin karışık Sonlu Eleman yöntemi Ile Serbest titreşim Analizi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 10, no. 1, 2021, pp. 319-27, doi:10.28948/ngumuh.823385.
Vancouver Ermiş M. Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. NOHU J. Eng. Sci. 2021;10(1):319-27.

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