Free Vibration Analysis of Prestressed Timoshenko Beams Using the Modal Analysis Method

• Autorzy: Nguyen Sy Nam , Nguyen Xuan Cuong , Nguyen Trung Hieu

Identyfikatory

DOI

10.12913/22998624/194145

• Języki publikacji: EN

Abstrakty

EN

Natural frequency and mode shape are important features in the dynamic analysis of beam structures. They are used in the analysis, design, and verification of beam structures. In dynamic problems, these characteristics influence the dynamic response of the beam. This study presents the equations for the free vibration analysis of prestressed Timoshenko beams and derives the characteristic equations to determine the natural frequencies and general mode functions using the modal analysis method. For each different boundary condition of the beam, the corresponding characteristic equations and eigenforms are then obtained. Using numerical methods, the change in natural frequencies is investigated and compared with the natural frequencies of ordinary Timoshenko beams and Euler-Bernoulli beams. As the beams undergo pre-compression, the gap in natural frequencies between the prestressed Timoshenko beam and the unstressed beam widens with increasing prestress. The natural frequency of the pre-tensioned beam is higher than that of the beam without pre-tension. This difference is most noticeable at the first order of the frequency, where it is most significant, but it decreases quickly as the frequency order rises.

Słowa kluczowe

EN

natural frequency; mode shape; Timoshenko beam; prestressed beam; modal function

• Wydawca: Lublin University of Technology ; Polish Society of Ecological Engineering (PTIE), Branch of PTIE in Lublin
• Czasopismo: Advances in Science and Technology. Research Journal
• Rocznik: 2024
• Tom: Vol. 18, no. 8
• Strony: 125--141
• Opis fizyczny: Bibliogr. 41 poz., fig., tab.

Twórcy

autor

Nguyen Sy Nam

• Hanoi University of Civil Engineering, Hanoi, Vietnam

• https://orcid.org/0009-0007-9218-0932

autor

Nguyen Xuan Cuong

• Hanoi University of Civil Engineering, Hanoi, Vietnam

• https://orcid.org/0000-0002-7271-7030

autor

Nguyen Trung Hieu

• Viet Architecture Joint Stock Company, Hanoi, Vietnam

Bibliografia

• 1. Hagedorn P. and DasGupta A. Vibrations and waves in continuous mechanical systems. John Woley&Sons, 2007.
• 2. Leissa A.W. and Qatu M.S. Vibration of Continuous Systems. McGraw-Hill, 2011.
• 3. Bottega W.J. Engineering Vibrations. CRC Press, 2006.
• 4. Meirovitch L. Analytical Methods in Vibrations. The Macmillan Company, 1967.
• 5. Gere J.M. and Timoshenko S.P. Mechanics of Materials. PWS Engineering, 1984.
• 6. Karacam F. and Aydogdu M. Wave propagation characteristics in functionally graded double-beams. Advances in Science and Technology Research Journal, 2017; 11(3): 143–49. doi:10.12913/22998624/76697.
• 7. Majkut L. Free and forced vibrations of Timoshenko beams described by single difference equation. Journal of theoretical and applied mechanics, 2009; 47(1): 193–210,.
• 8. Kim T., Park I., and Lee U. Forced vibration of Timoshenko beam subjected to stationary and moving loads using the modal analysis method. Shock and Vibration, 2017; 1–26, doi: 10.1155/2017/3924921.
• 9. Azam S.E., Mofid M. and Khoraskani R.A. Dynamic response of Timoshenko beam under moving mass. Scientia Iranica, Transaction A: Civil Engineering, 2013; 20(1): 50–56. doi: 10.1016/j. scient.2012.11.003.
• 10. Amiri A.M., Olfati A., Najjar S., Beiranvand P., Fard M.H.N. Study on flexural of reinforced geopolymer concrete beam. Advances in Science and Technology Research Journal, 2016; 10(30): 89–95. doi:10.12913/22998624/62630.
• 11. Al-Baijat H., Alhawamdeh M., and Khawaldeh A. Studying the flexural behavior of reinforced concrete beams under the effect of high temperature: Technology Research Journal, 2019; 13(2): 150–56. doi:10.12913/22998624/109055.
• 12. Piotrowski R. and Siedlecka M. Point protection of primary beams of steel grillages against lateral torsional buckling. Advances in Science and Technology Research Journal, 2020; 14(3): 1–8. doi:10.12913/22998624/121532.
• 13. Zhang Y., Cheng Y., Tan G., Lyu X., Sun X., Bai Y., and Yang S. Natural frequency response evaluation for RC beams affected by steel corrosion using acceleration sensors. Sensors, 2020; 20(18): 1–17. doi:10.3390/s20185335.
• 14. Zhang L., Sun L., and Dong L. Experimental study on the relationship between the natural frequency and the corrosion in reinforced concrete beams. Advances in materials science and engineering, 2021; 1–10. doi: 10.1155/2021/9976738.
• 15. Barrias A., Rodriguez G., Casas J.R., and Villalba S. Application of distributed optical fiber sensors for the health monitoring of two real structures in Barcelona. Structure and Infrastructure Engineering, 2018; 14(7): 967–985. doi: 10.1080/15732479.2018.1438479.
• 16. Kaloop M.R. and Li H. Monitoring of bridge deformation using GPS technique. KSCE Journal of Civil Engineering, 2009; 13(6): 423–431. doi: 10.1007/ s12205-009-0423-y.
• 17. Elhattab A., Uddin N., andObrien E. Drive-by bridge frequency identification under operational roadway speeds employing frequency independent underdamped pinning stochastic resonance (FI- UPSR). Sensors, 2018; 18(12): 1–22. doi: 10.3390/ s18124207.
• 18. Moradipour P., Chan T.H.T., and Gallage C. Benchmark studies for bridge health monitoring using an improved modal strain energy method. Procedia Engineering, 2017; 188: 194–200. doi: 10.1155/2017/3924921.
• 19. Magnon C., Galaup A., Rouffiac V., Opolon P., Connault E., Rosé M., Perricaudet M., Roche A., Germain S., Griscelli F., and Lassau N. Dynamic assessment of antiangiogenic therapy by monitor- ing both tumoral vascularization and tissue degeneration. Gene Therapy, 2007; 14(2): 108–117. doi: 10.1038/sj.gt.3302849.
• 20. Huong N.T.V., Nam N.S., Khang N.V. Numerical evaluation of the vibration response of a Timoshenko beam subjected to a moving force using the modal analysis approach, JST: Engineering and Technology for Sustainable Development, 2022; 32(1): 61–70, doi: 10.51316/jst.156.etsd.2022.32.1.9.
• 21. Roshandel D., Mofid M., and Ghannadiasl A. Modal analysis of the dynamic response of Timoshenko beam under moving mass. Scientia Iranica, Transaction A: Civil Engineering, 2015; 22(2): 331–344.
• 22. Abeles P.W. and Bardhan-Roy B.K. Prestressed Concrete Designer’s Handbook. 3rd edition, CRC Press, 1981.
• 23. Keer A.D. On the dynamic response of a prestressed beam. Princeton University Research Report, 1973.
• 24. Keer A.D. On the dynamic response of a prestressed beam. Journal of Sound and Vibration, 1976; 49(4): 569–573.
• 25. Saiidi M., Douglas B., Feng S. Prestress force effect on vibration frequency of concrete bridges. Journal of Structural Engineering, 1994; 120(7): 2233–2341. doi: 10.1061/(ASCE)0733-9445(1994)120:7(2233).
• 26. Fengge L. and Zhao Y. Finite element analysis of natural vibration frequency for unbounded prestressed concrete beams. Applied Mechanics and Materials, 2013; 351–352: 1034–1037. doi: 10.4028/www. scientific.net/AMM.351-352.1034.
• 27. Huong N.T.V. and Dien N.P. On the natural frequency and mode shape of a cracked and prestressed beam. Journal of Science and Technology (Technical Universities), 2014; 103: 47–52.
• 28. Huong N.T.V., Khang N.V., and Dien N.P. Dynamic response of a cracked and prestressed beam under the action of a moving body. Journal of Science and Technology (Technical Universities), 2015; 106: 58–62.
• 29. Jiang J. and Ye G. Dynamics of a prestressed Timoshenko beam subject to arbitrary external load, Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2010; 11(11): 898– 907. doi: 10.1631/jzus.A1000057.
• 30. Kien N.D. Free vibration of prestress Timoshenko beams resting on elastic foundation. Vietnam Journal of Mechanics, 2007; 29(1): 1–12. doi: 10.15625/0866-7136/29/1/5586.
• 31. Inman D.J. Engineering Vibration, 4th edition, Upper Saddle River, 2014.
• 32. Khatir A., Capozucca R., Khatir S., and Magagnini E. Vibration-based crack prediction on a beam model using hybrid butterfly optimization algorithm with artificial neural network. Frontiers of Structural and Civil Engineering, 2022; 16(8): 976–989. doi:10.1007/s11709-024-1079-x.A finite element model. Advances in Science and
• 33. Khatir A., Tehami M., Khatir S., and Wahab M.A. Multiple damage detection and localization in beam-like and complex structures using coordinate modal assurance criterion combined with firefly and genetic algorithms. Journal of Vibroengineering, 2016; 18(8): 5063–5073. doi: 10.21595/jve.2016.17026.
• 34. Raju P.M., Kumar M.P., Adiseshu S., and Kumar V.V.S.S. Mathematical Model for Natural Frequency of Prestressed Concrete beam using STAAD.Pro. In IOP Conference Series: Materials Science and Engineering, 1025(1): 012008, Vizianagaram, India, 15–16th November 2019. doi:10.1088/1757-899X/1025/1/012008.
• 35. Hamed E. and Frostig Y. Natural frequencies of bonded and unbonded prestressed beams-prestress force effects. Journal of Sound and Vibration, 2006; 29528–39. doi: 10.1016/j.jsv.2005.11.032.
• 36. Brecolotti M., Ubertini F., and Venanzi I. Natural frequencies of prestressed concrete beams: theoretical prediction and numerical validation. In: Proceeding of the XIX Aimeta Conference, 14–17, Ancona, Italy, 2009.
• 37. Belletti B. and Gasperi A. Behavior of prestressed steel beams. Journal of Structural Engineering, 2010; 136(9): 1131–39. doi:10.1061/(asce) st.1943-541x.0000208.
• 38. Gosaye J., Gardner L., Wadee M.A., and Ellen M.E. Compressive behaviour and design of prestressed steel elements. Structures, 2016; 5: 76–87. doi:10.1016/j.istruc.2015.09.001.
• 39. Hadjipantelis N., Gardner L., and Wadee M.A., A.M.ASCE. Finite-element modeling of prestressed cold-formed steel beams. Journal of Structural Engineering, 2019; 145(10): 1–19. doi:10.1061/(asce) st.1943-541x.0002375.
• 40. Hadjipantelis N., Gardner L., and Wadee M.A. Design of prestressed cold-formed steel beams. Thin-Walled Structures, 2019; 140: 565–78. doi:10.1016/j.tws.2019.02.029.
• 41. Reddy J.N. Energy principles and variational method in applied mechanics. John Wiley&Sons, 2002.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).