[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On the Nonlinear Thermomechanical Analysis of a Stayed-Beam Having Fractional Viscoelastic Properties in Complex Environment

Journal of Applied Nonlinear Dynamics 13(2) (2024) 351--371 | DOI:10.5890/JAND.2024.06.012

T.B. Djuitchou Yaleu, E.R. Fankem, B.R. Nana Nbendjo

Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaounde I P.O. Box 812, Yaounde, Cameroon

Download Full Text PDF

 

Abstract

In this paper, the nonlinear thermomechanical analysis of a stayed-beam made with fractional viscoelastic materials subjected to wind load and platoon motion loads under thermal conditions is investigated. Using Newton's second law of motion, the equation of dynamics is derived and reduced to generalized modal forms by applying the Galerkin methods. In the first vibration mode, the analytical study is conducted via multi-scale methods. Following this analytical procedure, the appearance conditions of various types of bifurcation are obtained using linear analysis; the periodic solutions are obtained using nonlinear analysis; then, the effect of fractional viscoelasticity, thermal variation and load spacing on the dynamics of the structure are explained numerically. It is found that, taking into account thermal loads due to temperature change in the environment, material properties and mechanical loads, many complex phenomena or loss of stability depending on the type of external loads can occurs. Thus, the advantageous effects of viscoelastic fractional derivative material, thermal and load spacing are established and it is also found that, depending on the type of loads, the fractional order changes the effect of thermal loads on the structure.

References

  1. [1]  Anague Tabejieu, L.M. (2017), On the dynamics of bridges subjected to service loads: roads traffic, train traffic and wind actions, PhD dissertation, Universite of Yaounde I, Cameroon.
  2. [2]  Abdel-Rohman, M. (2011), The influence of the higher order modes on the dynamic response of suspension bridges, Journal of Vibration and Control, 18(9), 1380-1405.
  3. [3]  Lenkei, P. (2007), Climate change and structural engineering, Periodica polytechnica Civil Engineering, 51(2), 47-50.
  4. [4]  Dlugoseci, A. et al (2009), Coping with Climate Change: Risks and opportunities for Insurers, Charted Insurance Institute, CII-3112, 31p, London.
  5. [5]  UNECE Expert group report (2013), Climate Change Impacts and Adaptation for International Transport Networks, United Nations, New York and Geneva, 248p.
  6. [6]  Lombardo, F.T. (2012), Improved extreme wind speed estimation for wind engineering applications, Journal of Wind Engineering and Industrial Aerodynamics, 104-106, 278-284.
  7. [7] Di Nino, S., Zulli, D., and Luongo, A. (2021), Nonlinear dynamics of an internally resonant base-isolated beam under turbulent wind flow, Applied Sciences, 11, 3213.
  8. [8]  Zhao, Y., Huanga, C., Chen, L., and Peng, J. (2018), Nonlinear vibration behaviors of suspended cables under two-frequency excitation with temperature effects, Journal of Sound and Vibration, 416, 279-294.
  9. [9]  Sohn, H., Dzwonczyk, M.,Straser, E.G., Kiremidjian, A.S., Law, K.H., and Meng, T. (1999), An experimental study of temperature effect on modal parameters of the Alamosa Canyon bridge, Earthquake Engineering and Structural Dynamics, 28, 879-897.
  10. [10]  Ding, Y.L. and Li, A.Q. (2011), Temperature-induced variations of measured modal frequencies of steel box girder for a long-span suspension bridge, International Journal of Steel Structures 11, 145-155.
  11. [11]  Djuitchou Yaleu, T.B., Metsebo, J., Nana Nbendjo, B.R., and Woafo, P. (2021), Effect of thermal and high static low dynamics stiffness isolator with the auxiliary system on a beam subjected to traffic loads, Journal of Vibration Engineering and Technologies, 1-12, https://doi.org/10.1007/42417-021-00399-3.
  12. [12]  Zhao, Y., Wang, Z., Zhang, X., and Chen, L. (2017), Effects of temperature variation on vibration of a cable-stayed beam,International Journal of Structural Stability and Dynamics, 17(10), 1750123.
  13. [13]  Zhang, J., Yang, X., and Dang, X. (2020), Research on Combination of Seismic and Temperature Action Effects of Multi-span Long Continuous Girder, 2020 International Conference on Intelligent Transportation, Big Data and Smart City, 327-331.
  14. [14]  Maleki S. and Maghsoudi-Barmi, A. (2016), Effects of concurrent earthquake and temperature loadings on cable-stayed bridges, International Journal of Structural Stability and Dynamics, 16(06), 1550020.
  15. [15]  Ge, Z.M. and Zhang, A.R. (2007), Chaos in a modified van der Pol system and in its fractional order systems, Chaos, Solitons and Fractals, 32(5), 1791-1822.
  16. [16]  Paola, M.D., Pinnola, F.P., and Zingales, M. (2013), A discrete mechanical model of fractional hereditary materials, Meccanica, 48(7), 1573-1586.
  17. [17]  Reyes-Melo, M.E., Gonz{a}lez-Gonz{a}lez, Guerrero-Salazar, C.A., Garc{i}a-Cavazos, F., and Ortiz-M{e}ndez, U. (2008), Application of fractional calculus to the modeling of the complex rheological behavior of polymers: From the glass transition to flow behavior. I. The theoretical model, Journal of Applied Polymer Science, 108(2), 731-737.
  18. [18]  Maia, N.M.M., Silva, J.M.M., and Ribeiro, A.M.R. (1998), On a general model for damping, Journal of Sound and Vibration, 218(5), 749-767.
  19. [19]  Tenreiro Machado, J.A., Silva, M.F., Barbosa, R.S., Jesus, I.S., Reis, C.M., Marcos, M.G., and Galhano, A.F. (2010), Some applications of fractional calculus in engineering, Mathematical Problems in Engineering, 2010, Article ID 639801, 34 pages.
  20. [20]  Xu, J., Chen, Y., Tai, Y., Xu, X., Shi, G., and Chen, N. (2020), Vibration analysis of complex fractional viscoelastic beam structures by the wave method, International Journal of Mechanical Sciences, 167, 105204.
  21. [21]  Nwagoum Tuwa, P.R., Miwadinou, C.H., Monwanou, A.V., Chabi Orou, J.B., and Woafo P. (2019), Chaotic vibrations of nonlinear viscoelastic plate with fractional derivative model and subjected to parametric and external excitations, Mechanics Research Communications, 97, 8-15.
  22. [22]  Abouelregal, A.E. (2020), Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation, Journal of Vibration and Control, 0(0), 1-13.
  23. [23]  Oumb{e} T{e}kam, G.T., Kitio Kwuimy, C.A., and Woafo, P. (2015), Analysis of tristable energy harvesting system having fractional order viscoelastic material, Chaos, 25, 013112.
  24. [24]  Mainardi F., (2010), Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London.
  25. [25]  Eldred, L.B., Baker, W.P., and Palazotto, A.N. (1995), Kelvin-Voigt vs fractional derivative model as constitutive relations for viscoelastic materials, American Institute of Aeronautics and Astronautics Journal, 33, 547-550.
  26. [26]  Anague Tabadjeu, L.M., Nana Nbendjo, B.R., and Filatrella, G. (2019), Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads, Chaos, Solitons and Fractals, 127, 178-188.
  27. [27]  Zhao, Y. and Huang,C. (2018), Temperature effects on nonlinear vibration behaviors of Euler-Bernoulli beams with different boundary conditions, Shock and Vibration, 6, 1-11.
  28. [28]  Karoumi, R. (1998), Response of cable-stayed and suspension bridges to moving vehicles: analysis methods and practical modeling techniques, PhD dissertation, Royal institute of technology, SE 10044 Stockholm, Sweden.
  29. [29]  Rossikhin, Y.A., Shitikova, M.V., Krusser, A.I. (2016), To the question on the correctness of fractional derivative models in dynamic problems of viscoelastic bodies, Mechanics Research Communications, 77, 44-49.
  30. [30]  Lewandowski, R. (2022), Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method, Meccanica, 57, 2337-2354.
  31. [31]  Ortigueira, M.D., Machado J.A.T. (2015), What Is a Fractional Derivative?, Journal of Computational Physics, 293, 4-13.
  32. [32]  Ortigueira, M.D., (2011), Fractional Calculus for Scientists and Engineers, Lecture Notes in Electrical Engineering, Springer, Berlin, Heidelberg.
  33. [33]  Samko, S., Kilbas, A., and Marichev, O. (1993), Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Amsterdam.
  34. [34]  Jekot, T. (1996), Nonlinear problems of thermal postbuckling of a beam, Journal of Thermal Stresses, 19, 359-367.
  35. [35]  Di Nino, S. and Louango, A. (2022), Nonlinear dynamics of a base-isolated beam under turbulent wind flow, Nonlinear Dynamics, 107, 1529-1544.
  36. [36]  Sun, L. and Feiquan, L. (2008), Steady-State Dynamic Response of a Bernoulli-Euler Beam on a Viscoelastic Foundation Subject to a Platoon of Moving Dynamic Loads, Journal of Vibration and Acoustics, 130(5), 051002(19 pages).
  37. [37]  Wahrhaftig, A.D.M., Silva, M.A.D., and Brasil, R.M.L.R.F. (2019), Analytical determination of the vibration frequencies and buckling loads of slender reinforced concrete towers, Latin American Journal of Solids and Structures, 16(05), https://doi.org/10.1590/1679-78255374.
  38. [38]  Kitio Kwimy, C.A., Nana Nbendjo, B.R., and Woafo, P. (2006), Optimization of electromechanical control of beam dynamics: Analytical method and finite differences simulation, Journal of Sound and Vibration, 298, 180-193.
  39. [39]  Liu, D., Xu, W., and Xu, Y. (2013), Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations, Acta Mechanica Sinica, 29(3), 443-51.
  40. [40]  Katembo, A.L. and Shitikova, M.V. (2019), Influence of fractional calculus model parameters on nonlinear forced vibrations of suspension bridges, IOP Conference Series: Materials Science and Engineering, 489, 012037.
  41. [41]  Nayfeh, A.H. and Mook, D.T. (1995), Nonlinear oscillations, Wiley, New York.
  42. [42]  Hayashi, C. (1964), Nonlinear Oscillations in Physical Systems, Mc Graw-Hill Inc, New York.
  43. [43]  Anague Tabadjeu, L.M., Nana Nbendjo, B.R., and Woafo, P. (2016), On the dyanamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads, Chaos, Solitons and Fractals, 93, 39-47.
  44. [44]  Luongo, A. and Zulli, D. (2011), Parametric external and self-excitation of a tower under turbulent wind flow, Journal of Sound and Vibration, 330, 3057-3069.
  45. [45]  Debnath, L. (2003), Recent applications of fractional calculus to science and engineering,International Journal of Mathematics and Mathematical Sciences, 54, 3413-3442.
  46. [46]  Petr{a}{\v{s}}, I. (2011), Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Beijing: Higher Education Press.
  47. [47]  Kang, H., Cong, Y., and Yan, G.G. (2020), Theoretical analysis of dynamic behaviors of cable-stayed bridges excited by two harmonic forces, Nonlinear Dynamics, https://doi.org/10.1007/s11071-020-05763-8.
  48. [48]  Abdel-Rohman, M. (2001), Effect of unsteady wind flow on galloping of tall prismatic structures, Nonlinear Dynamics, 26(3), 233-254.
  49. [49]  Robertson, I., Li, L., Sherwin, S.J., and Bearman, P.W. (2003), A numerical study of rotational and transverse galloping rectangular bodies, Journal of Fluids and Structures, 17(5), 681-699.
  50. [50]  Novak, M. (1972), Galloping oscillations of prismatic structures, Journal of Engineering Mechanics, 98(1), 27-46.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates