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

Yıl 2021, Cilt: 10 Sayı: 1, 319 - 327, 15.01.2021
https://doi.org/10.28948/ngumuh.823385

Öz

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

Kaynakça

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

Yıl 2021, Cilt: 10 Sayı: 1, 319 - 327, 15.01.2021
https://doi.org/10.28948/ngumuh.823385

Öz

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.

Kaynakça

  • Li W and Han B. Research and application of functionally gradient materials. IOP Conf. Series: Materials Science and Engineering 394, 1-7 2018. https://doi.org/ 10.1088/1757899X/394/2/022065.
  • M. R. Abbas, M. B. Uday, A. M. Noor, N. Ahmad and S. Rajoo, Microstructural evaluation of a slurry based Ni/YSZ thermal barrier coating for automotive turbocharger turbine application. Materials & Design, 109, 47-56, 2016. https://doi.org/10.1016/j.matdes. 2016.07.070
  • 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
  • K. B. Ghosh, J. Mukhopadhyay and R. N. Basu Functionally graded doped lanthanum cobalt ferrite and ceria-based composite interlayers for advancing the performance stability in solid oxide fuel cell. Journal of Power Sources, 328, 15-27, 2016. https://doi.org/10. 1016/j.jpowsour.2016.07.106
  • A. Solla, D. Bellucci and V. Cannillo, Functionally graded materials for orthopedic applications – an update on design and manufacturing. Biotechnology Advances 34, 504–531, 2016. https://doi.org/10.1016/ j.biotechadv.2015.12.013
  • J. Cherusseri, R. Scharma and K. K. Kar Helically coiled carbon nanotube electrodes for flexible supercapacitors. Carbon, 105, 113-125, 2016. https://doi.org/10.1016/j.carbon.2016.04.019
  • E. H. Egelman Three-dimensional reconstruction of helical polymers. Archives of Biochemistry and Biophysics, 581, 54-58, 2015. https://doi.org/10.1016 /j.abb.2015.04.004
  • X Jian, D. Wang, H. Liu, M. Jiang, Z. Zhou, J. Lu, X. Xu, Y. Wang, L. Wang, Z. Gong, M. Yang, J. Gou and D. Hui, Controllable synthesis of carbon coils and growth mechanism for twinning double-helix catalyzed by Ni nanoparticle. Composites Part B: Engineering, 61, 350-357, 2014. https://doi.org/10.1016/ j.compositesb.2013.06.010
  • A. Baratta and I. Corbi, Equilibrium models for helicoidal laterally supported staircases. Computers & Structures,124, 21-28, 2013. https://doi.org/10.1016/ j.compstruc.2012.11.007
  • M. Angelillo, Static analysis of a Guastavino helical stair as a layered masonry shell. Composite Structures 119, 298-304, 2015. https://doi.org/10.1016/ j.compstruct.2014.09.007
  • N. Gao and Y. Zhang, A low frequency underwater metastructure composed by helix metal and viscoelastic damping rubber. Journal of Vibration and Control, 25(3), 538-548, 2018. https://doi.org/10.1177/ 1077546318788446
  • N. Barbieri, R. Barbieri, R. A. da Silva, M. J. Mannala and L.S.A.V. Barbieri, Nonlinear dynamic analysis of wire-rope isolator and Stockbridge damper. Nonlinear Dynamics 86, 501-512, 2016. https://doi.org/10.1007/ s11071-016-2903-1
  • L. Wu, Q.-s. Wang and I. Elishakoff, Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode. Journal of Sound and Vibration, 284, 1190–1202, 2005. https://doi.org/10. 1016/j.jsv.2004.08.038
  • M. Aydogdu, Semi-inverse method for vibration and buckling of axially functionally graded beams. Journal of Reinforced Plastics and Composites, 27, 683–691 2008. https://doi.org/10.1177/0731684407081369
  • Shahba, R. Attarnejad, M. T. Marvi and S. Hajilar, Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions. Composites Part B: Engineering 42, 801–808, 2011. https://doi.org/10. 1016/j.compositesb.2011.01.017.
  • Y. Huang, L.-E. Yang and Q.-Z. Luo, Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section. Composites Part B: Engineering 45, 1493–1498, 2013. https://doi.org/10. 1016/j.compositesb.2012.09.015
  • 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
  • V. Yıldırım, A parametric study on the free vibration of noncylindrical helical springs. Journal of Applied Mechanics, 65(1), 157-163, 1998. https://doi.org/10. 1115/1.2789019
  • W. Busool and M. Eisenberger, Free vibration of helicoidal beams of arbitrary shape and variable cross section. Journal of Vibration and Acoustic, 124, 397–409, 2002. https://doi.org/10.1115/1.1468870
  • V. Yıldırım, A parametric study on the natural frequencies of unidirectional composite conical springs. Communications in Numerical Methods in Engineering, 20, 207–227, 2004. https://doi.org/10.10 02/cnm.661
  • J. Lee, Free vibration analysis of non-cylindrical helical springs by the pseudospectral method. Journal of Sound and Vibration 305, 543–551, 2007. https://doi.org/10.1016/j.jsv.2006.11.008
  • A. Yu and Y. Hao, Effect of warping on natural frequencies of symmetrical cross-ply laminated composite non-cylindrical helical springs. International Journal of Mechanical Sciences, 74, 65–72 (2013). https://doi.org/10.1016/j.ijmecsci.2013.04.010
  • N. Eratlı, M. Ermis, M. H. Omurtag, Free vibration analysis of helicoidal bars with thin-walled circular tube cross-section via mixed finite element method. Sigma Journal of Engineering and Natural Sciences, 33, 200–218, 2015.
  • N. Eratli, M. Yilmaz, K. Darilmaz and M.H. Omurtag, Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM. Structural Engineering and Mechanics, 57, 221–238, 2016. https://doi.org/10. 12989/sem.2016.57.2.221.
  • F. F. Çalım, Dynamic analysis of composite coil springs of arbitrary shape. Composites Part B: Engineering, 40, 741–757, 2009. https://doi.org/ 10.10 16/j.compositesb.2009.04.017.
  • F. F. Çalım, Forced vibration of helical rods of arbitrary shape. Mechanics Research Communications, 36, 882–891, 2009. https://doi.org/10.1016/j.mechrescom.2009 .07.007.
  • A. Yampolsky and A. Opariy, Generalized helices in three-dimensional Lie groups. Turkish Journal of Mathematics, 43, 1447–1455, 2019.
  • Ü. Çiftçi, A generalization of Lancret’s theorem, J. Geom. Phys. 59, 1597–1603, 2009. https://doi.org/10. 1016/j.geomphys.2009.07.016.
  • M. Ermis and M.H. Omurtag, Static and dynamic analysis of conical helices based on exact geometry via mixed FEM. International Journal of Mechanical Sciences, 131, 296–304, 2017. https://doi.org/10. 1016/j.ijmecsci.2017.07.010.
  • M. Ermis, Static and dynamic analysis of non-circular helical bars based on exact geometry. Ph. D Thesis, Istanbul Technical University, İstanbul, Türkiye 2019.
  • C.S. Jog, I.S. Mokashi, A finite element method for the Saint-Venant torsion and bending problems for prismatic beams. Computers & Structures, 135, 62–72 2014. https://doi.org/10.1016/j.compstruc.2014.01.0 10
  • R. Barretta, L. Feo and R. Luciano, Some closed-form solutions of functionally graded beams undergoing nonuniform torsion. Composite Structures, 123, 132–136, 2015. https://doi.org/10.1016/j.compstruct.2014. 12.027
  • K. Darılmaz, E. Orakdögen and K. Girgin, Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach. Acta Mechanica, 229, 1387–1398, 2018. https://doi.org/10.1007/s00707-017-2067-1
  • U. N. Aribas Kompozit eğrisel kirişlerde kesit çarpilmasi gözetilerek normal ve kayma gerilmelerinin karışık sonlu elemanlarla analizi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 8(3), 16-29, 2019. https://doi.org/10.28948/ngumuh. 619591
  • U. N. Aribas, M. Ermis, N. Eratli and M. H. Omurtag, The static and dynamic analyses of warping included composite exact conical helix by mixed FEM. Composites Part B: Engineering, 160, 285–297, 2019. https://doi.org/10.1016/j.compositesb.2018.10.018
  • U. N. Aribas, M. Ermis, A. Kutlu , N. Eratli and M. H. Omurtag, Forced vibration analysis of composite-geometrically exact elliptical cone helices via mixed FEM. Mechanics of Advanced Materials and Structures, 1-19, 2020. https://doi.org/10.1080/ 15376494.2020.1824048.
  • H.C. Tsai and J. M. Kelly, Buckling of short beams with warping effect included, International Journal of Solids and Structures. 42(1), 239–253, 2005. https://doi.org/10.1016/j.ijsolstr.2004.07.021
  • Genoese, A. Genoese, A. Bilotta and G. Garcea, A geometrically exact beam model with non-uniform warping coherently derived from the Saint Venant rod. Engineering Structures 68, 33–46, 2014. https://doi.org/10.1016/j.engstruct.2014.02.024
  • K. Yoon, P. S. Lee and D. N. Kim, Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects. Composite Structures 132, 1231–1247, 2015. https://doi.org/ 10.1016/j.compstruct.2015.07.024
  • Di Egidio, A. Contento and F. Vestroni, The role of nonlinear torsional contributions on the stability of flexural–torsional oscillations of open-cross section beams. Journal of Sound and Vibration 358, 236–250 2015. https://doi.org/10.1016/j.jsv.2015.08.004
  • ANSYS®, Academic Research Mechanical, Release 17.1, Canonsburg, Pennsylvania, 2016.
  • M. H. Omurtag and A. Y. Aköz, The mixed finite element solution of helical beams with variable cross-section under arbitrary loading.. Computers & Structures, 43, 325–331, 1992. https://doi.org/10.1016/ 0045-7949 (92)90149-T.
  • J.T. Oden and J.N. Reddy, An introduction to the mathematical theory of finite elements, John Wiley & Sons, Limited, 1976.
Toplam 63 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İnşaat Mühendisliği
Bölüm İnşaat Mühendisliği
Yazarlar

Merve Ermiş 0000-0003-0201-6586

Yayımlanma Tarihi 15 Ocak 2021
Gönderilme Tarihi 9 Kasım 2020
Kabul Tarihi 16 Aralık 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 10 Sayı: 1

Kaynak Göster

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. NÖHÜ Müh. Bilim. Derg. Ocak 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, sy. 1 (Ocak 2021): 319-27. https://doi.org/10.28948/ngumuh.823385.
EndNote Ermiş M (01 Ocak 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”, NÖHÜ Müh. Bilim. Derg., c. 10, sy. 1, ss. 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 (Ocak 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. NÖHÜ Müh. Bilim. Derg. 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, c. 10, sy. 1, 2021, ss. 319-27, doi:10.28948/ngumuh.823385.
Vancouver Ermiş M. Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi. NÖHÜ Müh. Bilim. Derg. 2021;10(1):319-27.

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