ELASTİK ZEMİN ve MANYETİK ALAN ETKİSİ ALTINDAKİ KADEMELİ KİRİŞİN DOĞRUSAL TİTREŞİM ANALİZİ

Öz

Teknolojideki gelişmelerle birlikte farklı kiriş türlerine olan gereksinim artmaktadır. Yaygın olarak kullanılan farklı kiriş türlerinden bir tanesi de kademeli kirişlerdir. Sunulan bu çalışmada önemli yapısal elemanlardan birisi olan kirişin kademeli olması durumu ele alınmıştır. Kademe sayısı olarak tek kademeli durum dikkate alınmış olup kademe oranı ve konumu irdelenmiştir. Çalışmanın temel motivasyon kaynağı kademeli kirişin elastik zemin üzerinde olması ve manyetik alana maruz kalmasıdır. Kademeli kiriş üzerine doğrusal elastik zemin katsayının ve manyetik alan kuvvetinin etkilerini içeren kapsamlı bir çalışma yürütülmüştür. Farklı mesnet durumları da incelenerek çalışmanın zenginliği arttırılmıştır. Belirtilen değişken parametrelerin doğal frekanslar üzerine etkileri üç boyutlu grafikler halinde sunulmuştur. Manyetik alan ve elastik zemin etkisinin doğal frekanslar üzerine önemli bir etkiye sahip olduğu görülmüştür. Kademe oranı ve konumunun etkisi serbest serbest sınır şartlarında en etkili olmasına karşın manyetik alan ve elastik zemin etkisi ankastre serbest sınır şartına sahip durumda daha belirgin olmaktadır.

Anahtar Kelimeler

• Elastik Zemin
• Kademeli Kiriş
• Manyetik Alan
• Pertürbasyon Tekniği
• Sürekli Ortam Mekaniği

LINEAR VIBRATION ANALYSIS OF STEPPED BEAM UNDER THE EFFECT OF ELASTIC FOUNDATION AND MAGNETIC FIELD

Öz

The necessity of different beam types is increasing with the advances in technology. One of the different types of beams commonly used is stepped beams. In this context, the presented study deals with the stepped beam, which is one of the essential structural elements. The one-stage situation was taken into account and the stage ratio and position were examined. The main source of motivation for the study is that the stepped beam is on the elastic ground and exposed to a magnetic field. A comprehensive study was carried out on the effects of linear elastic foundation coefficient and magnetic field on the stepped beam. The richness of the study has been increased by examining different support situations. The effects of the specified variable parameters on natural frequencies are presented in three-dimensional graphics. It has been observed that the magnetic field and elastic ground effect have a significant effect on natural frequencies. Although the effect of step ratio and position is most effective in the free-free boundary conditions, the magnetic field and elastic ground effect are more explicit in the case of fixed-free boundary conditions.

Anahtar Kelimeler

• Continuum Mechanics
• Elastic Foundation
• Magnetic Field
• Perturbation Technique
• Stepped Beam

Kaynakça

1. Arani, A. G., Dashi, P., Amir, S., Yousefi, M., 2015. Nonlinear vibration of coupled nano- and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field. Acta Mech, 226, 2729–2760. doi 10.1007/s00707-015-1342-2
2. Atcı, D., 2021. Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory. Z Naturfr. A, 76(5), 427–434. https://doi.org/10.1515/zna-2020-0335
3. Atcı, D., Bağdatlı, S. M., 2017. Vibrations of fluid conveying microbeams under non-ideal boundary conditions. Microsyst Technol., 23, 4741–4752. https://doi.org/10.1007/s00542-016-3255-y,
4. Atcı, D., Bağdatlı, S. M., 2018. Principle parametric resonance of fluid conveying microbeams under non-ideal boundary conditions. El-Cezerî J Sci Eng., 5(2),671–680.
5. Bağdatlı, S. M., Özkaya, E., Özyiğit, H. A., Tekin A., 2009. Nonlinear vibrations of stepped beam systems using artificial neuralnetworks. Structural Engineering And Mechanics, 33(1), 15-30. doi: 10.12989/sem.2009.33.1.015
6. Bert, C.W., Newberry, A.L., 1986. Improved finite element analysis of beam vibration. Journal of Sound and Vibration, 105(1), 179-183.
7. Chang, T-P., 2016. Nonlinear free vibration analysis of nanobeams under magnetic field based on nonlocal elasticity theory. Journal of Vibroengıneering, 18(3). ISSN 1392-8716 http://dx.doi.org/10.21595/jve.2015.16751
8. Cheng, P., Davila, C., Hou, G., 2014. Static, Vibration Analysis and Sensitivity Analysis of Stepped Beams Using Singularity Functions, 234085. https://doi.org/10.1155/2014/234085

9. Chicurel R. and Suppiger E., 1961. A tabular collocation method for beam vibration. Journal of Engineering for Industry, Transactions of the ASME 83, 373-376. https://doi.org/10.1115/1.3664534
10. Esen, I., Abdelrhmaan, A.A., Eltaher, M.A., 2022. Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields. Engineering with Computers 38, 3463–3482. https://doi.org/10.1007/s00366-021-01389-5
11. Jandaghian A. A., Rahmani O., 2016. Free vibration analysis of magneto-electro-thermoelastic nanobeams resting on a Pasternak foundation. Smart Mater. Struct., 25, 035023.
12. Jang, S. K., and Bert, C. W., 1989. Free vibration of stepped beams: Exact and numerical solutions. Journal of Sound and Vibration, 130(2), 342–346. doi:10.1016/0022-460x(89)90561-0
13. Kural, S., 2018. Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam. Tech J., 12(1),18–26. https://doi.org/ 10.31803/tg-20180131225708
14. Kural, S., 2020. Effect of spring mid-support condition on the vibrations of the axially moving string. Int Adv Res Eng J., 4(3),191–199. https://doi.org/10.35860/iarej.757503
15. Kural, S., Özkaya, E., 2015. Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation. J Vib Control, 23(7),1106–1114. https://doi.org/10.1177/1077546315589666
16. Lee, J., Bergman, L. A., 1994. The vibration of stepped beams and rectangular plates by an elemental dynamic flexibility method. Journal of Sound and Vibration, 171(5), 617–640. https://doi.org/10.1006/jsvi.1994.1145
17. Lu Z. R., Huang M., Liu, J. K., Chen, W. H., Liao, W. Y., 2009. Vibration analysis of multiple-stepped beams with the composite element model. Journal of Sound and Vibration, 322 (4-5), 1070–1080.
18. Naguleswaran, S., 2003. Vibration and stability of an Euler–Bernoulli beam with up to three-step changes in cross-section and in axial force. International Journal of Mechanical Sciences, 45(9), 1563-1579.
19. Nalbant, M. O., Bagdatli, S. M., Tekin, A. 2023. Free Vibrations Analysis of Stepped Nanobeams Using Nonlocal Elasticity Theory. Scientia Iranica. 10.24200/sci.2023.61602.7395.
20. Nešić N., Kozić P., Janevski G., 2022. Modes Of Non-Homogeneous Damped Beams On A Winkler-Type Elastic Layer. Innovatıve Mechanıcal Engıneerıng, 2(1), 130-152.
21. Özkaya, E., Tekin, A., 2007. Nonlinear vibrations of stepped beam system under different boundary conditions. Structural Engineering and Mechanics, 27 (3), 333–345. https://doi.org/10.12989/SEM.2007.27.3.333
22. Taleb, N. J., Suppiger, E. W., 1961. Vibrations of stepped beams. Journal of Aerospace Engineering, 28, 295-298.
23. Tang, Y., Ma, Z-S, Ding, Q., Wang, T., 2021. Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: A nano-structure analysis. Composite Structures. 264, 113746. https://doi.org/10.1016/j.compstruct.2021.113746
24. Taşkın, V., Varserin, İ., Demirhan, P. A., 2021. Değişken Kesitli Kirişlerin Genel Sınır Şartları İçin Titreşim Analizi. Trakya Üniversitesi Mühendislik Bilimleri Dergisi, 22(2), 73-86.
25. Tekin, A., Özkaya, E., Bağdatlı, S. M., 2009. Three-to-one internal resonance in multiple stepped beam systems. Appl. Math. Mech. -Engl. Ed. 30(9), 1131–1142. doi: 10.1007/s10483-009-0907-x
26. Wang, J., 1991. Vibration of stepped beams on elastic foundations. Journal of Sound and Vibration, 149(2), 315-322. https://doi.org/10.1016/0022-460X(91)90640-6
27. Yapanmış, B. E, Bagdatlı S. M., 2022. Investigation of the nonlinear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam. Z Naturfr A. https://doi.org/10.1515/zna-2021-0300.
28. Yapanmış, B. E., 2022. Nonlinear Vibration and Internal Resonance Analysis of Microbeam with Mass Using the Modified Coupled Stress Theory. Journal of Vibration Engineering and Technologies, https://doi.org/10.1007/s42417-022-00694-7