Mekanik Bir Sistemin Bir Ters Rezonans Frekansının Kütle Eklenerek Değiştirilmesi

Year 2018, Volume: 30 Issue: 2, 127 - 134, 19.09.2018

Orhan Çakar

Abstract

Ters rezonans frekansı mekanik sistemlerin dinamik
özelliklerinden biridir ve frekans tepki fonksiyonu grafiklerinde ters tepeler
olarak gözükürler. Bir yapı belirli bir noktadan ters rezonans frekansındaki
harmonik bir kuvvet ile tahrik edildiğinde yapının belirli noktaları titreşim
hareketi yapmayabilir. Bu bakımdan bazı titreşim problemlerinin çözümünde bu
özellikten faydalanılmaktadır. Bu çalışmada mevcut bir sistemin noktasal veya
çapraz frekans tepki fonksiyonlarında belirli bir ters rezonansı kütle eklemek
suretiyle başka bir frekansa kaydırma üzerine bir yöntem sunulmuştur. Yöntem
matematikten bilinen Sherman-Morrison formülüne dayalı olup orijinal sistemin
frekans tepki fonksiyonlarını kullanmaktadır. Bu yöntem sistemin fiziksel
özelliklerinin veya modal özelliklerinin bilinmesine gerek duymadığından
oldukça avantajlıdır. Yöntemin geçerliliği ve etkinliği altı serbestlik
dereceli bir sistem üzerinde gerçekleştirilen çeşitli sayısal uygulamalarla
gösterilmiştir. 

Keywords

Titreşim, Ters rezonans, Doğal frekans, Yapısal değişiklik, Frekans Tepki Fonksiyonu, Sherman-Morrison formülü

References

• 1. Özgüven H. N. (1990). Structural Modifications Using Frequency Response Functions. Mechanical Systems and Signal Processing, 4(1):53-63. 2. Bucher I. and Braun S. (1993). The Structural modification inverse problem: An exact solution. Mechanical Systems and Signal Processing, 7(3): 217-238. 3. Sivan D.D. and Ram Y. M. (1996). Mass and Stiffness Modifications to Achieve Desired Natural Frequencies. Comm. in Numerical Methods in Engineering, 12: 531-542. 4. Chang K.J., and Park Y.P. (1998). Substructural Dynamic Modification using Component Receptance Sensitivity. Mechanical Systems and Signal Processing, 12: 525-541. 5. Tao L. and Jimin H. (1999). Local structural modification using mass and stiffness changes. Engineering Structures, 21(11):1028-1037. 6. Park Y.H., and Park Y.S. (2000). Structural Modification Based on Measured Frequency Response Functions: An Exact Eigenproperties Reallocation. Journal of Sound and Vibration, 237(3): 411-426. 7. Ram Y.M. (2000). Dynamic Structural Modification. The Shock and Vibration Digest, 32(1): 11-17. 8. Braun S. G., and Ram Y. M. (2001). Modal Modification of Vibrating Systems: Some Problems and Their Solutions. Mechanical Systems and Signal Processing, 15(1):101-119. 9. Tsuei Y. G. and Yee E. K. L.(1989). A method for modifying dynamic properties of undamped mechanical systems. ASME Journal of Dynamic Systems, Measurement and Control, 111:403-408. 10. Ram Y.M. (1994). Enlarging a spectral gap by structural modification. Journal of Sound and Vibration, 176(2):225-234. 11. McMillan J., and Keane A. J. (1996). Shifting resonances from a frequency band by applying concentrated masses to a thin rectangular plate. Journal of Sound and Vibration, 192 (2):549-562. 12. Kyprianou A., Mottershead JE. and Ouyang H. (2004). Assignment of natural frequencies by an added mass and one or more springs. Mechanical Systems and Signal Processing, 18:263–289. 13. Farahani K. and Bahai H. (2004). An inverse strategy for relocation of eigenfrequencies in structural design. Part I: first order approximate solutions. Journal of Sound and Vibration, 274:481–505. 14. Lawther R. (2007). Assessing how changes to a structure can create gaps in the natural frequency spectrum. International Journal of Solids and Structures, 44:614–635. 15. Ouyang H., Richiedei D., Trevisani A. and Zanardo G. (2012). Eigenstructure assignment in undamped vibrating systems: a convex-constrained modification method based on receptances. Mechanical Systems and Signal Processing, 27(2):397–409. 16. Ouyang H., Richiedei D., Trevisani A. and Zanardo G. (2012). Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: Theory and experimental validation. International Journal of Mechanical Sciences, 64: 211–220. 17. Ouyang H. and Zhang J. (2015). Passive modifications for partial assignment of natural frequencies of mass-spring systems. Mechanical Systems and Signal Processing. 50-51:214-226. 18. Liu Z., Li W., Ouyang H. and Wang D. (2015). Eigenstructure assignment in vibrating systems based on receptances. Archive of Applied Mechanics, 85:713-724. 19. Çakar, O. (2017). Bir sistemin doğal frekanslarının kütle eklenerek kaydırılması üzerine bir çalışma. 18.Ulusal Makine Teorisi Sempozyumu-UMTS2017, (5-7 Temmuz 2017) Bildirileri, M. İtik (Editör), Trabzon, 381-386. 20. Mottershead J. E. (1999). On the zeros of structural frequency response functions and their sensitivities, Mechanical Systems and Signal Processing, 12(5): 591-597. 21. Mottershead J. E. and Lallement G. (1999). Vibration Nodes, and the Cancellation of Poles and Zeros by Unit-Rank Modifications to Structures. Journal of Sound and Vibration, 222(5):833-851. 22. Mottershead J. E. (2001). Structural Modification for the Assignment of Zeros Using Measured Receptances. ASME Journal of Applied Mechanics, 68: 791-798. 23. Mottershead J. E., Mares C., and Friswell M. I. (2001). An inverse method for the assignment of vibration nodes. Mechanical Systems and Signal Processing, 15(1):87-100. 24. Prells, U., Mottershead, J.E. and Friswell, M.I. (2003). On Pole–Zero Placement By Unit-Rank Modifıcation. Mechanical Systems and Signal Processing, 17(3): 611-633. 25. Sherman J. and Morrison W.J. (1950). Adjustment of an Inverse Matrix Corresponding to a Change in one Element of a Given Matrix. Annals of Mathematical Statistics, 21(1):124-127. 26. Akgün M.A., Garcelon J.H., and Haftka R.T. (2001). Fast Exact Linear and Non-Linear Structural Reanalysis and the Sherman-Morrison-Woodbury Formulas. Int. J. for Numerical Methods in Engineering, 50: 1587-1606. 27. Çakar O. (2011). Mass and stiffness modifications without changing any specified natural frequency of a structure. Journal of Vibration and Control, 17(5):769–776. 28. Sanliturk K.Y. (2002). An Efficient Method for Linear and Nonlinear Structural Modifications. Proceedings of ESDA 2002: 6th Biennial Conference on Engineering Systems Design and Analysis, ESDA 2002/APM-028, (8-11, July 2002), Istanbul, Turkey.