Trapez Hız Profilinin Ayarlanması Yoluyla Hareketli Bir Kütle Altındaki Kirişin Titreşim Kontrolü

Abstract

Bu makalede, hareketli bir kütleye sahip basit mesnetli bir kirişin artık titreşimi incelenmiştir. Kütle kiriş üzerinde başlangıç noktasından bitiş noktasına ivmelenen, sabit hız ve yavaşlayan zaman aralıklarına sahip trapez hız profili ile hareket etmektedir. Kütle durduktan sonra kirişin orta noktasının artık titreşimi analiz edilir. Sistemin matematiksel modeli, sonlu elemanlar (FE) teorisi kullanılarak geliştirilmiştir. Hareketli kütle nedeniyle zamana bağlı matrislere sahip FE modelinin çözümü için Newmark yöntemi kullanılmıştır. Model, çözüm sonuçları ile literatürde daha önce yapılan çalışmalarda verilen sonuçlar karşılaştırılarak doğrulanmıştır. Sistemin doğal frekansı ile hareket eden kütlenin hız profili arasındaki ilişkinin yapının artık titreşimi üzerinde etkili olduğu gözlemlenmiştir. Hareketli kütle durma konumunda iken sistemin doğal frekansı ile hareket eden kütlenin yavaşlama zaman aralığının tersi eşit ise artık titreşimler minimum seviyede oluşur. Doğru hız profili seçimi ile titreşim seviyelerindeki düşüşün hareket sırasında %70'e, durduktan sonra ise %80'e yaklaştığı gözlemlenmiştir.

Keywords

• Hareketli kütle
• basit mesnetli kiriş
• titreşim kontrolü
• sonlu elemanlar analizi
• Newmark yöntemi

Vibration Control of A Beam Under A Moving Mass Through Adjusting Trapezoidal Velocity Profile

Abstract

In this article, the residual vibration of a simply supported beam with a moving mass is studied. The mass moves from a starting point to an end point on the beam with a trapezoidal velocity profile having accelerating, constant velocity and decelerating time intervals. The residual vibration of the mid-point of the beam after the mass stops is analyzed. The mathematical model of the system is developed using the finite element (FE) theory. Newmark method is used for the solution of FE model having time dependent matrices because of the moving mass. The model is verified by comparing the solution results with the results given in the previous studies in the literature. It is seen that the relationship between the natural frequency of the system and the velocity profile of the moving mass has an effect on the residual vibration of the structure. If the natural frequency of the system and the inverse of the deceleration time interval of the moving mass are equal while the moving mass is at the stopping position, residual vibrations occur at a minimum level. It seen that with the right speed profile selection, the decrease in vibration levels approaches 70% during the movement and 80% after stopping.

Keywords

• Moving mass
• simply supported beam
• vibration control
• finite element analysis
• Newmark method

References

1. Akdağ M. and Şen H. (2021) S-curve motion profile design for vibration control of single link flexible manipulator. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 23(68): 661-676.
2. Ankaralı A. and Diken H. (1997) Vibration control of an elastic manipulator link. Journal of Sound and Vibration, 204(1): 162-170.
3. Assie A., Akbas S.D., Bashiri H.B., Abdelrahman A.A. and Eltaher M.A. (2021) Vibration response of perforated thick beam under moving load. Eurepean Physical Journal Plus, 136(283): 15 pages.
4. Dimitrovova Z. (2017) New semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation. International Journal of Mechanical Sciences, 127: 142–162.
5. Dyniewicz B., Bajer C.A., Kuttler K.A. and Shillor M. (2019) Vibrations of a Gao beam subjected to a moving mass. Nonlinear Analysis: Real World Applications, 50: 342–364.
6. Ebrahimi-Mamaghani A., Sarparast H. and Masoud R. (2020) On the vibrations of axially graded Rayleigh beams under a moving load. Applied Mathematical Modelling, 84: 554–570.
7. Esmailzadeh E. and Ghorashi M. (1995) Vibration analysis of beams traversed by uniform partially distributed moving masses. Journal of Sound and Vibration, 184 (1): 9–17.
8. Foyouzat M.A., Estekanchi H.E. and Mofid M. (2018) An analytical-numerical solution to assess the dynamic response of viscoelastic plates to a moving mass. Applied Mathematical Modelling, 54: 670–696.

9. Freidani M. and Hosseini M. (2020) Elasto-dynamic response analysis of a curved composite sandwich beam subjected to the loading of a moving mass. Mechanics of Advanced Composite Structures, 7: 347–354.
10. Ganjefar S., Rezaei S. and Pourseifi M. (2015). Self-adaptive vibration control of simply supported beam under a moving mass using self-recurrent wavelet neural networks via adaptive learning rates. Meccanica, 50(12): 2879- 2898. Golovin I. (2021) Model-based control for active damping of crane structural vibrations. PhD Thesis, Fakultat fur Elektrotechnik und Informationstechnik der Otto-von-Guericke-Universitat, Magdeburg.
11. Golovin I. and Palis S. ¬(2019) Robust control for active damping of elastic gantry crane vibrations. Mechanical Systems and Signal Processing, 121: 264–278
12. Golovin I. and Palis S. ¬(2020)¬ Modeling and discrepancy based control of underactuated large gantry cranes. IFAC PapersOnLine, 53(2):7783–7788
13. Hamza G., Barkallah M., Hammadi M., Choley J. and Riviere A. (2020) Predesign of a flexible multibody system excited by moving load using a mechatronic system approach. Mechanics & Industry, 21(604): 9 pages.
14. Karagülle H., Malgaca L., Dirilmiş M., Akdağ M. and Yavuz Ş. (2017) Vibration control of a two-link flexible Manipulator. Journal of Vibration and Control, 23(12): 2023–2034.
15. Kiani Y. (2017) Dynamics of FG-CNT reinforced composite cylindrical panel subjected to moving load. Thin-Walled Structures, 111: 48–57
16. Li H., Le M.D., Gong Z.M., Lin W. (2009) Motion profile design to reduce residual vibration of high-speed positioning stages. IEEE/ASME Transactions On Mechatronics, 14(2):264-269
17. Liu C., Chen Y. (2018) Combined S-curve feedrate profiling and input shaping for glass substrate transfer robot vibration suppression. Industrial Robot: An International Journal 45/4: 549–560
18. Malgaca L., Yavuz Ş., Akdağ M. and Karagülle H. (2016) Residual vibration control of a single-link flexible curved manipulator. Simulation Modelling Practice and Theory, 67: 155-170.
19. Mohanty A., Varghese M.P. and Behera R.K. (2019) Coupled nonlinear behavior of beam with a moving mass. Applied Acoustics, 156: 367–377.
20. Newmark NM (1959) A method of computation for structural dynamics. Journal of Engineering Mechanics, ASCE 85: 67–94.
21. Nguyen Q.C., Ngo H.Q.T. (2016) Input shaping control to reduce residual vibration of a flexible beam. Journal of Computer Science and Cybernetics, 32(1): 73–88
22. Rezaei S. and Pourseifi M. (2018) vibration suppression of simply supported beam under a moving mass using on-line neural network controller. Journal of Solid Mechanics, 10(2):387-399.
23. Ryu B., and Kong Y. (2012) dynamic responses and active vibration control of beam structures under a travelling mass. In Advances on Analysis and Control of Vibrations-Theory and Applications: 231-252.
24. Seifoori S., Parrany A.H. and Darvishinia S. (2021) Experimental studies on the dynamic response of thin rectangular plates subjected to moving mass. Journal of Vibration and Control 27(5-6): 685-697.
25. Thomson W.T. and Dahleh M.D. (1988) Theory of vibration with applications, (3rd edition). Englewood Cliffs: Prentice-Hall.
26. Xin Y., Xu G., Su N. and Dong Q. (2018) Nonlinear vibration of ladle crane due to a moving trolley. Hindawi Mathematical Problems in Engineering: 4, 1-14 pages.
27. Wu J.J. (2008) Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element. International Journal of Mechanical Sciences 50 (4): 613–625.
28. Yavuz Ş., Malgaca L. and Karagülle H. (2016) Vibration control of a single-link flexible composite manipulator. Composite Structures : 140: 684-691
29. Zhang X., Thompson D. and Sheng X. (2020) Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam. Journal of Sound and Vibration 481 (115432): 14 pages.
30. Zrnic N., Gasic V., Bosnjak S. and Dordevic M. (2013). Moving loads in structural dynamics of cranes: bridging the gap between theoretical and practical researches. FME Transactions 41(4): 291-297.