EFFECT OF THE FINITE ELEMENT MODELING TECHNIQUES ON THE DYNAMIC ANALYSIS OF BEAMS

Yıl 2022, Cilt: 9 Sayı: 18, 581 - 590, 31.12.2022

Ahmad Reshad Noorı , Sefa Yıldırım

https://doi.org/10.54365/adyumbd.1173315

Cited By: 1

Öz

Analysis of the free and forced vibration responses of beams is one of the most critical problems to be examined in the design step of these structural members. The finite-element method which solves boundary value problems can be applied efficiently to vibration problems. In this study, the natural vibration frequency and damped and undamped transient analyses of the pinned-pinned beams are investigated. The well-known finite-element software packages, ANSYS and SAP2000, are used. The 2-D elastic beam which is based on the Euler-Bernoulli Beam theory, 3-D two-node and 3-D three-node beam elements which are based on Timoshenko beam theory, and four-node shell elements are used in ANSYS and the frame member is utilized in SAP2000. The effect of these elements on the dynamic behaviors of the isotropic beam is discussed. The results are given in tabular and graphical form for the free and forced vibration, respectively.

Anahtar Kelimeler

Free Vibration, Forced Vibration, Beam, Finite-Element Method, Viscoelastic

SONLU ELEMAN MODELLEME TEKNİKLERİNİN KİRİŞLERİN DİNAMİK ANALİZİNE ETKİSİ

Öz

Kirişlerin serbest ve zorlanmış titreşim davranışlarının analizi, bu yapı elemanlarının tasarım aşamasında incelenmesi gereken en kritik problemlerden biridir. Sınır değer problemlerini çözen sonlu elemanlar yöntemi, titreşim problemlerine de etkin bir şekilde uygulanabilir. Bu çalışmada, iki ucundan sabit mesnetli kirişlerin doğal titreşim frekansları ile sönümlü ve sönümsüz zorlanmış titreşim analizleri incelenmiştir. Analizlerde, iyi bilinen sonlu eleman yazılım paket programları ANSYS ve SAP2000 kullanılmıştır. ANSYS'te Euler-Bernoulli Kiriş teorisine dayanan 2 boyutlu elastik kiriş, Timoshenko kiriş teorisine dayanan 3 boyutlu iki düğümlü ile 3 boyutlu üç düğümlü kiriş elemanları ve dört düğümlü kabuk elemanlar kullanılırken SAP2000'de ise çerçeve elemanı kullanılmıştır. Bu elemanların izotropik kirişin dinamik davranışları üzerindeki etkisi tartışılmıştır. Sonuçlar, serbest ve zorlanmış titreşim için sırasıyla tablo ve grafik şeklinde verilmiştir.

Anahtar Kelimeler

Serbest Titreşim, Zorlanmış Titreşim, Kiriş, Sonlu Elemanlar Yöntemi, Viskoelastik

Kaynakça

• Kapur KK. Vibrations of a Timoshenko beam, using finite‐element approach. The Journal of the Acoustical Society of America 1966;40:1058–63. https://doi.org/10.1121/1.1910188.
• Thomas J, Abbas BAH. Finite element model for dynamic analysis of Timoshenko beam. Journal of Sound and Vibration 1975;41:291–9. https://doi.org/10.1016/S0022-460X(75)80176-3.
• Gupta RS, Rao SS. Finite element eigenvalue analysis of tapered and twisted Timoshenko beams. Journal of Sound and Vibration 1978;56:187–200. https://doi.org/10.1016/S0022-460X(78)80014-5.
• Dawe DJ. A finite element for the vibration analysis of Timoshenko beams. Journal of Sound and Vibration 1978;60:11–20. https://doi.org/10.1016/0022-460X(78)90397-8.
• Chen AT, Yang TY. Static and dynamic formulation of a symmetrically laminated beam finite element for a microcomputer. Journal of Composite Materials. 1985;19(5):459-475. doi:10.1177/002199838501900505
• Ahmed KM. Free vibration of curved sandwich beams by the method of finite elements. Journal of Sound and Vibration 1971;18:61–74. https://doi.org/10.1016/0022-460X(71)90631-6.
• Yang F, Sedaghati R, Esmailzadeh E. Free in-plane vibration of general curved beams using finite element method. Journal of Sound and Vibration 2008;318:850–67. https://doi.org/10.1016/J.JSV.2008.04.041.
• Ramtekkar GS. Free vibration analysis of delaminated beams using mixed finite element model. Journal of Sound and Vibration 2009;328:428–40. https://doi.org/10.1016/J.JSV.2009.08.008.
• Ramtekkar GS, Desai YM, Shah AH. Natural vıbrations of laminated composite beams by using mixed finite element modelling. Journal of Sound and Vibration 2002;257:635–51. https://doi.org/10.1006/JSVI.2002.5072.
• Alshorbagy AE, Eltaher MA, Mahmoud FF. Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling 2011;35:412–25. https://doi.org/10.1016/J.APM.2010.07.006.
• Jafari AA, Eftekhari SA. A new mixed finite element-differential quadrature formulation for forced vibration of beams carrying moving loads. Journal of Applied Mechanics, Transactions ASME 2011;78:0110201–01102016. https://doi.org/10.1115/1.4002037/465703.
• Yang H, Lo SH, Sze KY, Leung AYT. Coupled static and dynamic buckling of thin walled beam by spline finite element. Thin-Walled Structures 2012;60:118–26. https://doi.org/10.1016/J.TWS.2012.07.012.
• Özütok A, Madenci E. Free vibration analysis of cross-ply laminated composite beams by mixed finite element formulation. International journal of structural stability and dynamics 2013;13. https://doi.org/10.1142/S0219455412500563.
• Javid M, Hemmatnezhad M. Finite element formulation for the large-amplitude vibrations of FG beams. Archive of Mechanical Engineering 2014;61:469--482. https://doi.org/10.2478/MECENG-2014-0027.
• Vo TP, Thai HT, Nguyen TK, Maheri A, Lee J. Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering Structures 2014;64:12–22. https://doi.org/10.1016/J.ENGSTRUCT.2014.01.029.
• Rakowski J, Guminiak M. Non-linear vibration of Timoshenko beams by finite element method. Journal of Theoretical and Applied Mechanics 2015;53:731–43. https://doi.org/10.15632/JTAM-PL.53.3.731.
• Tekili S, Youcef K, Merzoug B. Finite element analysis of free vibration of beams with composite coats. Mechanika 2015;21:290–295–290–295. https://doi.org/10.5755/J01.MECH.21.4.9849.
• Shang Hsu Y. Enriched finite element methods for Timoshenko beam free vibration analysis. Applied Mathematical Modelling 2016;40:7012–33. https://doi.org/10.1016/J.APM.2016.02.042.
• Kahya V, Turan M. Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering2017;109:108–15. https://doi.org/10.1016/J.COMPOSITESB.2016.10.039.
• Hui Y, Giunta G, Belouettar S, Huang Q, Hu H, Carrera E. A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements. Composites Part B: Engineering2017;110:7–19. https://doi.org/10.1016/J.COMPOSITESB.2016.10.065.
• Karkon M. An efficient finite element formulation for bending, free vibration and stability analysis of Timoshenko beams. Journal of the Brazilian Society of Mechanical Sciences and Engineering 2018;40:1–16. https://doi.org/10.1007/S40430-018-1413-0/TABLES/6.
• Eroglu U, Tufekci E. A new finite element formulation for free vibrations of planar curved beams. Mechanics Based Design of Structures and Machines 2018;46:730–50. https://doi.org/10.1080/15397734.2018.1456343.
• Nguyen DK, Tran TT. Free vibration of tapered BFGM beams using an efficient shear deformable finite element model. Steel and Composite Structures 2018;29:363–77. https://doi.org/10.12989/SCS.2018.29.3.363.
• Pegios IP, Hatzigeorgiou GD. Finite element free and forced vibration analysis of gradient elastic beam structures. Acta Mechanica 2018 229:12 2018;229:4817–30. https://doi.org/10.1007/S00707-018-2261-9.
• Mechanical APDL Element Reference, 2013, Inc., 275 Technology Drive, Canonsburg, PA 15317.
• Analysis Reference Manual For SAP2000®, ETABS®, SAFE® and CSiBridge, Computers & Structures, 1978-2016.
• Li XF. A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and Vibration 2008;318:1210–29. https://doi.org/10.1016/J.JSV.2008.04.056.