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Investigation on dynamic stability of Timoshenko beam using axial parametric excitation

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Abstract

Vibration mitigation has been an important research interest in the past decades. In this paper, the enhancement of vibration suppression of thick beams is investigated. The Timoshenko beam is considered, and finite element method is used to discretize governing equations for the beam consisting of axial load. The stability of the system is studied both numerically by using Floquet theory, and analytically by employing averaging perturbation method. Effects of the thickness change, also boundary conditions are provided. The results demonstrate that, by adding extra boundary condition, the stability of the beam increases under the same circumstances. It means that, boundary condition can play important role in mitigating the vibration. Moreover, considering the thick beam reveals that the equivalent damping of the beam enhances. In this case, the excitation amplitude as well as the excitation frequency will increase. Therefore, under the same condition, the thicker the beam is, the more stable it will be.

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References

  1. K.K. Żur, N. Firouzi, T. Rabczuk, X. Zhuang, Large deformation of hyperelastic modified Timoshenko-Ehrenfest beams under different types of loads. Comput. Methods Appl. Mech. Eng. 416, 116368 (2023)

    ADS  MathSciNet  Google Scholar 

  2. T.Q. Thai, X. Zhuang, T. Rabczuk, Curved flexoelectric and piezoelectric micro-beams for nonlinear vibration analysis of energy harvesting. Int. J. Solids Struct. 264, 112096 (2023)

    Google Scholar 

  3. L. He, H. Guo, Y. Jin, X. Zhuang, T. Rabczuk, Y. Li, Machine-learning-driven on-demand design of phononic beams. Sci. China Phys. Mech. 65, 214612 (2022)

    Google Scholar 

  4. A. Shishegaran, B. Karami, T. Rabczuk, A. Shishegaran, M.A. Naghsh, M. Mohammad Khani, Performance of fixed beam without interacting bars. Front. Struct. Civ. Eng. 14, 1180–1195 (2020)

    Google Scholar 

  5. F. Dadgar-Rad, N. Firouzi, Large deformation analysis of two-dimensional visco-hyperelastic beams and frames. Arch. Appl. Mech. 91, 4279–4301 (2021)

    ADS  Google Scholar 

  6. S. Sarfarazi, R. Shamass, I. Mascolo, G.D. Corte, F. Guarracino, Some considerations on the behaviour of bolted stainless-steel beam-to-column connections: a simplified analytical approach. Metals 13, 753 (2023)

    Google Scholar 

  7. S. Sarfarazi, R. Shamass, G.D. Corte, F. Guarracino, Assessment of design approaches for stainless-steel joints through an equivalent FE modelling technique. Ce/Papers 5, 271–281 (2022)

    Google Scholar 

  8. A. Mojahedin, M. Jabbari, T. Rabczuk, Thermoelastic analysis of functionally graded porous beam. J. Therm. Stresses 41, 937–950 (2018)

    Google Scholar 

  9. B. Akgöz, Ö. Civalek, Buckling analysis of functionally graded tapered microbeams via Rayleigh-Ritz method. Mathematics 10, 4429 (2022)

    Google Scholar 

  10. B. Karami, M. Janghorban, T. Rabczuk, Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory. Compos. B Eng. Eng. 182, 107622 (2020)

    Google Scholar 

  11. Ö. Civalek, B. Uzun, M.O. Yayli, An effective analytical method for buckling solutions of a restrained FGM nonlocal beam Comput. Appl. Math. 41, 67 (2022)

    Google Scholar 

  12. J. Kim, K.K. Żur, J.N. Reddy, Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos. Struct. 209, 879–888 (2019)

    Google Scholar 

  13. A.I. Aria, M.I. Friswell, A nonlocal finite element model for buckling and vibration of functionally graded nanobeams. Compos. B Eng. Eng. 166, 233–246 (2019)

    Google Scholar 

  14. K. Alambeigi, M. Mohammadimehr, M. Bamdad, T. Rabczuk, Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation. Acta Mech. 231, 3199–3218 (2020)

    MathSciNet  Google Scholar 

  15. H. Babaei, K.K. Żur, Effect of thermal pre/post-buckling regimes on vibration and instability of graphene-reinforced composite beams. Eng. Anal. Bound. Element 152, 528–539 (2023)

    MathSciNet  Google Scholar 

  16. C. Hameury, G. Ferrari, A. Buabdulla, T.M.P. Silva, P. Balasubramanian, G. Franchini, M. Amabili, Multiple-input multiple-output active vibration control of a composite sandwich beam by fractional order positive position feedback. Mech. Syst. Signal Process. 200, 110633 (2023)

    Google Scholar 

  17. H.B. Khaniki, M.H. Ghayesh, S. Hussain, M. Amabili, Effects of geometric nonlinearities on the coupled dynamics of CNT strengthened composite beams with porosity, mass and geometric imperfections. Eng. Comput. 38, 3463–3488 (2022)

    Google Scholar 

  18. ŞD. Akbaş, H. Ersoy, B. Akgöz, Ö. Civalek, Dynamic analysis of a fiber-reinforced composite beam under a moving load by the Ritz method. Mathematics 9, 1048 (2021)

    Google Scholar 

  19. H. Farokhi, M.H. Ghayesh, M. Amabili, Nonlinear resonant behavior of microbeams over the buckled state. Appl. Phys. A 113, 297–307 (2013)

    ADS  Google Scholar 

  20. M.H. Ghayesh, M. Amabili, Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam. Compos. B Eng. Eng. 60, 371–377 (2014)

    Google Scholar 

  21. S.N.H. Hosseini, Y.T. Beni, Free vibration analysis of rotating piezoelectric/flexoelectric microbeams. Appl. Phys. A 129, 330 (2023)

    ADS  Google Scholar 

  22. M.H. Ghayesh, H. Farokhi, M. Amabili, In-plane and out-of-plane motion characteristics of microbeams with modal interactions. Compos. B Eng. Eng. 60, 423–439 (2014)

    Google Scholar 

  23. M.H. Ghayesh, M. Amabili, H. Farokhi, Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams. Int. J. Eng. Sci. 71, 1–14 (2013)

    MathSciNet  Google Scholar 

  24. P. Jankowski, K.K. Żur, J. Kim, J.N. Reddy, On the bifurcation buckling and vibration of porous nanobeams. Compos. Struct. 250, 112632 (2020)

    Google Scholar 

  25. B. Uzun, Ö. Civalek, M.Ö. Yaylı, Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mech. Based Des. Struct. Mach. 51, 481–500 (2023)

    Google Scholar 

  26. P. Jankowski, K.K. Żur, J. Kim, C.W. Lim, J.N. Reddy, On the piezoelectric effect on stability of symmetric FGM porous nanobeams. Compos. Struct. 267, 113880 (2021)

    Google Scholar 

  27. B. Uzun, Ö. Civalek, M.Ö. Yaylı, A hardening nonlocal approach for vibration of axially loaded nanobeam with deformable boundaries. Acta Mech. 234, 2205–2222 (2023)

    MathSciNet  Google Scholar 

  28. A.I. Aria, M.I. Friswell, T. Rabczuk, Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis. Compos. Struct. 212, 118–128 (2019)

    Google Scholar 

  29. B. Uzun, Ö. Civalek, M.Ö. Yaylı, Nonlinear stability analysis of embedded restrained nanobeams using the Stokes’ transformation. Mech. Based Des. Struct. Mach. (2023). https://doi.org/10.1080/15397734.2023.2185633

    Article  Google Scholar 

  30. J. Marzbanrad, M. Boreiry, G.R. Shaghaghi, Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect. Appl. Phys. A 122, 691 (2016)

    ADS  Google Scholar 

  31. R. Ansari, M. FarajiOskouie, S. Nesarhosseini et al., Flexoelectricity effect on the size-dependent bending of piezoelectric nanobeams resting on elastic foundation. Appl. Phys. A 127, 518 (2021)

    ADS  Google Scholar 

  32. A. Norouzzadeh, R. Ansari, H. Rouhi, Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach. Appl. Phys. A 123, 330 (2017)

    ADS  Google Scholar 

  33. H.M. Numanoğlu, H. Ersoy, B. Akgöz, Ö. Civalek, A new eigenvalue problem solver for thermo-mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method. Math. Methods Appl. Sci. 45, 2592–2614 (2022)

    ADS  MathSciNet  Google Scholar 

  34. M. Fakher, S. Hosseini-Hashemi, Vibration of two-phase local/nonlocal Timoshenko nanobeams with an efficient shear-locking-free finite-element model and exact solution. Eng. Comput. 38, 231–245 (2022)

    Google Scholar 

  35. M.A. Eltaher, A.A. Abdelrahman, A. Al-Nabawy, M. Khater, A. Mansour, Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position. Appl. Math. Comput. 235, 512–529 (2014)

    MathSciNet  Google Scholar 

  36. Ç. Demir, K. Mercan, H.M. Numanoglu, Ö. Civalek, Bending response of nanobeams resting on elastic foundation. J. Appl. Comput. Mech. 4, 105–114 (2018)

    Google Scholar 

  37. Ö. Civalek, O. Kiracioglu, Free vibration analysis of Timoshenko beams by DSC method. Int. J. Numer. Methods Biomed. Eng. 26, 1890–1898 (2010)

    Google Scholar 

  38. T. Rabczuk, J. Eibl, Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element approach. Int. J. Solids Struct. 41, 1061–1080 (2004)

    Google Scholar 

  39. T. Rabczuk, G. Zi, Numerical Fracture analysis of prestressed concrete beams. Int. J. Concr. Struct. Mater. 2, 153–160 (2008)

    Google Scholar 

  40. B. Painter, G. Ferrari, M. Amabili, Nonlinear vibrations of beams with Bouc-Wen hysteretic boundary conditions. Nonlinear Dyn. 108, 2903–2916 (2022)

    Google Scholar 

  41. H.B. Khaniki, M.H. Ghayesh, R. Chin, M. Amabili, Large amplitude vibrations of imperfect porous-hyperelastic beams via a modified strain energy. J. Sound Vib. 513, 116416 (2021)

    Google Scholar 

  42. P. Balasubramanian, G. Franchini, G. Ferrari, B. Painter, K. Karazis, M. Amabili, Nonlinear vibration of beams with bilinear hysteresis at supports: interaction of experimental results. J. Sound Vib. 499, 115998 (2021)

    Google Scholar 

  43. E. Loghman, F. Bakhtiari-Nejad, A. Kamali, M. Abbaszadeh, M. Amabili, Nonlinear vibration of fractional viscoelastic micro-beams. Int. J. Non-Linear Mech. 137, 103811 (2021)

    ADS  Google Scholar 

  44. A. Tondl, Some Problems of Rotor Dynamics (Chapman and Hall, London, 1965)

    Google Scholar 

  45. A. Tondl, To the problem of quenching self-excited vibrations. Acta Tech. CSAV 43, 109–116 (1998)

    Google Scholar 

  46. F. Dohnal, Damping of mechanical vibrations by parametric excitation, PhD thesis, Vienna University of Technology, Austria, 2005.

  47. F. Dohnal, Suppressing self-excited vibrations by synchronous and time-periodic stiffness and damping variation. J. Sound Vib. 306, 136–152 (2007)

    ADS  MathSciNet  Google Scholar 

  48. F. Dohnal, Damping by parametric stiffness excitation: resonance and anti-resonance. J. Vibrat. Control 14, 669–688 (2008).

    MathSciNet  Google Scholar 

  49. F. Dohnal, Experimental studies on damping by parametric excitation using electromagnets, Proc. Inst. Mech. Eng. Pt. C J. Mechan. Eng. Sci. 226, 2015–2027 (2012).

  50. F. Dohnal, H. Ecker, H. Springer, Enhanced damping of a cantilever beam by axial parametric excitation. Arch. Appl. Mech. 78, 935–947 (2008)

    ADS  Google Scholar 

  51. F. Dohnal, F. Verhulst, Averaging in vibration suppression by parametric stiffness excitation. Nonlinear Dyn. 54, 231–248 (2008)

    MathSciNet  Google Scholar 

  52. Z. Kulesza, J.T. Sawicki, Damping by parametric excitation in a set of reduced-order cracked rotor systems. J. Sound Vib. 354, 167–179 (2015)

    ADS  Google Scholar 

  53. J-S. Bae, J-H. Hwang, J-H. Roh, J-H. Kim, M-S. Yi, J-H. L, Vibration suppression of a cantilever beam using magnetically tuned-mass-damper. J. Sound Vib. 331, 5669–5684 (2012).

  54. I.F. Lazar, S.A. Neild, D.J. Wagg, Vibration suppression of cables using tuned inerter dampers. Eng. Struct. 122, 62–71 (2016)

    Google Scholar 

  55. Z. Kraus, A. Karev, P. Hagedorn, F. Dohnal, Enhancing vibration mitigation in a Jeffcott rotor with active magnetic bearings through parametric excitation. Nonlinear Dyn. 109, 393–400 (2022)

    Google Scholar 

  56. K.-J. Bathe, Finite Element Procedures (Prentice Hall, 1996)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Structural Mechanics, Bauhaus-University, Weimar, Germany

    Nasser Firouzi

  2. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    Sayyed Roohollah Kazemi

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  1. Nasser Firouzi
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  2. Sayyed Roohollah Kazemi
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Contributions

Conceptualization, formulation derivation and analyses were performed by Nasser Firouzi. The first draft of the manuscript was written by Nasser Firouzi. Supervision and also editing the manuscript were done by Sayyed Roohollah Kazemi. All authors commented on previous versions of the manuscript and approved the final manuscript.

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Correspondence to Nasser Firouzi or Sayyed Roohollah Kazemi.

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Firouzi, N., Kazemi, S.R. Investigation on dynamic stability of Timoshenko beam using axial parametric excitation. Appl. Phys. A 129, 869 (2023). https://doi.org/10.1007/s00339-023-07155-2

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