Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Structural health monitoring through nonlinear frequency-based approaches for conservative vibratory systems

  • Bayat, M. (Department of Civil and Environmental Engineering, University of Pittsburgh) ;
  • Pakar, I. (Department of Civil Engineering, Faculty of Engineering, Shomal University) ;
  • Ahmadi, H.R. (Department of Civil Engineering, Faculty of Engineering, University of Maragheh) ;
  • Cao, M. (Jiangxi Provincial Key Laboratory of Environmental Geotechnical Engineering and Disaster Control, Jiangxi University of Science and Technology) ;
  • Alavi, A.H. (Department of Civil and Environmental Engineering, University of Pittsburgh)
  • Received : 2019.03.21
  • Accepted : 2019.10.25
  • Published : 2020.02.10
⟨ Previous Next ⟩

Abstract

This paper proposes a new approximate analytical solution for highly nonlinear vibration of mechanical systems called Hamiltonian Approach (HA) that can be widely use for structural health monitoring systems. The complete procedure of the HA approach is studied, and the precise application of the presented approach is surveyed by two familiar nonlinear partial differential problems. The nonlinear frequency of the considered systems is obtained. The results of the HA are verified with the numerical solution using Runge-Kutta's [RK] algorithm. It is established the only one iteration of the HA leads us to the high accurateness of the solution.

Keywords

Acknowledgement

Supported by : Swanson School of Engineering at the University of Pittsburgh

References

  1. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  2. Avazpour, L. (2018), "Fractional Ostrowski type inequalities for functions whose derivatives are prequasiinvex", J. Inequal. Spec. Funct., 9, 15-29.
  3. Avazpoura, L., Allahviranloob, T. and Islamc, S. (2016), "Uncertain Hermite-Hadamard inequality for functions with (s, m)-Godunova-Levin derivatives via fractional integral", J. Nonlinear Sci. Appl. (JNSA), 9(5).
  4. Avci, O., Bhargava, A., Al-Smadi, Y. and Isenberg, J. (2018), "Vibrations serviceability of a medical facility floor for sensitive equipment replacement: evaluation with sparse in situ data", Practice Periodical Struct. Design Construct., 24(1), 05018006. https://doi.org/10.1061/(asce)sc.1943-5576.0000404
  5. Bayat, M. and Pakar, I. (2015), "Mathematical solution for nonlinear vibration equations using variational approach", Smart Struct. Syst., 15(5), 1311-1327. https://doi.org/10.12989/sss.2015.15.5.1311.
  6. Bayat, M., Pakar, I. and Bayat, M. (2017a), "Nonlinear vibration of multi-body systems with linear and nonlinear springs", Steel Compos. Struct., 25(4), 49b7-503. https://doi.org/10.12989/scs.2017.25.4.497.
  7. Bayat, M., Pakar, I. and Cao, M.S. (2017b), "Energy based approach for solving conservative nonlinear systems", Earthq. Struct., 13(2), 131-136. https://doi.org/10.12989/eas.2017.13.2.131.
  8. Bennamia, I., Badereddine, A. and Zebbiche, T. (2018), "Measurement of vibrations of composite wings using highorder finite element beam", J. Measurement. Eng., 6(3), 143-154. https://doi.org/10.21595/jme.2018.20046.
  9. Dehghani, E., Zadeh, M.N. and Nabizadeh, A. (2019), "Evaluation of seismic behaviour of railway bridges considering track-bridge interaction", Roads Bridges-Drogi i Mosty, 18(1), 51-66. http://dx.doi.org/10.7409/rabdim.019.004.
  10. Deng, T. (2018), "Simplified method and influence factors of vibration characteristics of isolated curved girder bridge", Struct. Durability Health Monitor., 12(3), 189-212. https://doi.org/10.3970/sdhm.2018.04392.
  11. Ellis, D., Tabatabai, H. and Nabizadeh, A. (2018), "Residual tensile strength and bond properties of GFRP bars after exposure to elevated temperatures", Materials, 11(3), 346. https://doi.org/10.3390/ma11030346.
  12. Feng, H., Liu, G., Yuan, J., Sheikh, M. N., Feng, L. and Zhao, J. (2019), "Influence of Water Stability on Bond Performance Between Magnesium Phosphate Cement Mortar and Steel Fibre", Struct. Durability Health Monitor., 13(1), 105-121. https://doi.org/10.32604/sdhm.2019.04864.
  13. Ganji, S.S, Ganji, D.D., Ganji, Z.Z. and Karimpour, S. (2009), "Periodic solution for strongly nonlinear vibration systems by He's energy balance method", Acta Applicandae Mathematicae, 106(1), 79. https://doi.org/10.1007/s10440-008-9283-6.
  14. Golafshani, A.A., Kia, M. and Alanjari, P. (2013), "Local joint flexibility element for offshore plateforms structures", Marine Struct., 33, 56-70. https://doi.org/10.1016/j.marstruc.2013.04.003.
  15. Hashemiparast, S. and Avazpour, L. (2008), "Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations", AIP Conference Proceedings, 1048, 257. https://doi.org/10.1063/1.2990906.
  16. He, J.H. (2008), "Max-min approach to nonlinear oscillators", J. Nonlinear Sci. Numeric. Simul., 9(2), 207-210. https://doi.org/10.1515/IJNSNS.2008.9.2.207.
  17. He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314. https://doi.org/10.1016/j.physleta.2010.03.064.
  18. Hieu, D.V. (2018), "Postbuckling and free nonlinear vibration of microbeams based on nonlinear elastic foundation", Math. Problems Eng., 2018. https://doi.org/10.1155/2018/1031237.
  19. Hosseinzadeh, K., Alizadeh, M. and Ganji, D.D. (2018), "Hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates by analytical method", J. Mech. Mater. Eng., 13(1), 4. https://doi.org/10.1186/s40712-018-0089-7.
  20. Jalili, P., Ganji D.D. and Nourazar, S. (2018), "Hybrid semi analytical method for geothermal U shaped heat exchanger", Case Studies Therm. Eng., 12, 578-586. https://doi.org/10.1016/j.csite.2018.07.010.
  21. Jamshidi, L. and Avazpour, L. (2012), "Solution of the fuzzy boundary value differential equations under generalized differentiability by shooting method", J. Fuzzy Set Valued Anal., 136, 1-19. https://doi.org/10.5899/2012/jfsva-00136.
  22. Johnson, D., Darzi, M., Ulishney, C., Bade, M. and Zamani, N. (2017), "Methods to Improve Combustion Stability, Efficiency, and Power Density of a Small, Port-Injected, Spark-Ignited, Two-Stroke Natural Gas Engine", ASME 2017 Internal Combustion Engine Division Fall Technical Conference, American Society of Mechanical Engineers Digital Collection. https://doi.org/10.1115/ICEF2017-3557.
  23. Joubari, M., Mehdi, M., Ganji, D.D. and Javanian Jouybari, H. (2014), "Determination of periodic solution for tapered beams with modified iteration perturbation method", J. Appl. Comput. Mech., 1(1), 44-51. https://dx.doi.org/10.22055/jacm.2014.10729.
  24. Kalita, K. and Haldar, S. (2015), "Parametric study on thick plate vibration using FSDT", Mech. Mech. Eng., 19(2), 81-90.
  25. Kalita, K. and Haldar S. (2016), "Free vibration analysis of rectangular plates with central cutout", Cogent Eng., 3(1), 1163781. https://doi.org/10.1080/23311916.2016.1163781.
  26. Kia, M. and Banazadeh, M. (2016), "Closed-form fragility analysis of the steel moment resisting frames", Steel Compos. Struct., 21(1), 93-107. http://dx.doi.org/10.12989/scs.2016.21.1.093.
  27. Kroworz, A. and Katunin, A. (2018), "Non-Destructive Testing of Structures Using Optical and Other Methods: A Review", Struct. Durability Health Monitor., 12(1), 1-1.
  28. Kutanaei, S.S. and Choobbasti, A.J. (2019), "Prediction of liquefaction potential of sandy soil around a submarine pipeline under earthquake loading", J. Pipeline Systems Eng., 10(2), 04019002. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000349.
  29. Lu, X. and Memari, A. (2019), "Comparative Energy Analysis and Life-Cycle Assessment of Innovative Residential Wall Systems in Cold Regions", Practice Periodical Struct. Design Construct., 24(3), 04019015. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000432.
  30. Mackie, K.R. and Scott, M.H. (2019), "Implementation of Nonlinear Elements for Seismic Response Analysis of Bridges", Practice Periodical Struct. Design Construct., 24(3), 04019011. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000420.
  31. Martinez, M.M. and Echeverria Valiente, E.E. (2019), "Methodological Contribution of KW Johansen to Structural Analysis of Long Cylindrical Roof Shells: Beam Method", Practice Periodical on Structural Design and Construction, 24(4), 04019022. http://hdl.handle.net/10017/38633. https://doi.org/10.1061/(asce)sc.1943-5576.0000436
  32. Nayfeh, A.H. (2011), Introduction to Perturbation Techniques, John Wiley and Sons, New Jersey, U.S.A.
  33. Olvera, D. and Elias-Zuniga, A. (2014), "Enhanced multistage homotopy perturbation method: Approximate solutions of nonlinear dynamic systems", Abstract Appl. Analysis, 2014, 486509. https://doi.org/10.1155/2014/486509.
  34. Sarokolayi, L.K., Kutanaei S.S., Golafshani, S.M.I., Haji, S.R.H. and Mashhadban, H. (2016), "Control-volume-based finite element modelling of liquefaction around a pipeline", Geomatics, Natural Hazards Risk, 7(4), 1287-1306. https://doi.org/10.1080/19475705.2015.1060638.
  35. Sun, W., Sun, Y., Yu, Y. and Zheng, S. (2016), "Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method", Struct. Eng. Mech., 59(1), 1-14. http://dx.doi.org/10.12989/sem.2016.59.1.001.
  36. Suresh, L. and Mini, K.M. (2019), "Effect of multiple tuned mass dampers for vibration control in high-rise buildings", Practice Periodical Struct. Design Construct., 24(4), 04019031. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000453.
  37. Tee, K.F. (2018), "Time series analysis for vibration-based structural health monitoring: A review", Struct. Durability Health Monitor., 12(3), 129-147. https://doi.org/10.3970/sdhm.2018.04316.
  38. Wu, Y., Cheng, Q., Yang, G. and Dai, J. (2019), "Research on vibration characteristics of a multi-barrel artillery", J. Vibroeng., 21(5), 1241-1250. https://doi.org/10.21595/jve.2019.20037.
  39. Zangooee, M., Hosseinzadeh, K. and Ganji, D.D. (2019), "Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM", Case Studies Therm. Eng., 14, 100460. https://doi.org/10.1016/j.csite.2019.100460.
  40. Zhang, D. and Wang, S. (2018), "Nonlinear effect of tooth-slot transition on axial vibration, contact state and speed fluctuation in traveling wave ultrasonic motor", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(19), 3424-3438. https://doi.org/10.1177/0954406217736551.
  41. Zhao, L. and Wu, Y.P. (2019), "Active vibration control of rotating beam with moving mass using piezoelectric actuator", J. Vibroeng., 21(5). https://doi.org/10.21595/jve.2019.20017.
  42. Zhuang, M., Miao, C. and Chen, R. (2019), "Load Test and Fatigue Life Evaluation for Welded Details in Taizhou Yangtze River Bridge", Struct. Durability Health Monitor., 13(2), 205-225. https://doi.org/10.32604/sdhm.2019.04654

Cited by

  1. Analytical model of shape memory alloy embedded smart beam, under actuated condition vol.27, pp.6, 2020, https://doi.org/10.12989/sss.2021.27.6.991