Steel and Composite Structures

  • 제25권4호
  • /
  • Pages.497-503
  • /
  • 2017
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear vibration of multi-body systems with linear and nonlinear springs

  • Bayat, Mahmoud (Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University) ;
  • Pakar, Iman (Young Researchers and Elite club, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahdi (Department of Civil Engineering, Roudehen Branch, Islamic Azad University)
  • 투고 : 2016.12.19
  • 심사 : 2017.09.20
  • 발행 : 2017.11.20
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.

키워드

참고문헌

  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. Bayat, M., Bayat, M. and Pakar, I. (2015a), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232. https://doi.org/10.12989/eas.2015.9.1.221
  3. Bayat, M. and Pakar, I. (2015b), "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
  4. Bayat, M., Pakar, I. and Domaiirry, G. (2012), "Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review", Latin Am. J. Solid. Struct., 9(2), 145-234.
  5. Chen, G. (1987), "Applications of a generalized Galerkin's method to non-linear oscillations of two-degree-of-freedom systems", J. Sound Vib., 119, 225-242. https://doi.org/10.1016/0022-460X(87)90451-2
  6. Cveticanin, L. (2001), "Vibrations of a coupled two-degree-offreedom system", J. Sound Vib., 247, 279-292. https://doi.org/10.1006/jsvi.2001.3728
  7. Cveticanin, L. (2002). "The motion of a two-mass system with non-linear connection", J. Sound Vib., 252, 361-369. https://doi.org/10.1006/jsvi.2000.3551
  8. HashemiKachapi, S.M. and Ganji, D.D. (2013), Dynamics and Vibrations: Progress in Nonlinear Analysis, Springer 2013.
  9. He, J.H. (1999), "Variational iteration method: a kind of nonlinear analytical technique: some examples", Int. J. Nonlinear Mech., 34(4), 699-708 https://doi.org/10.1016/S0020-7462(98)00048-1
  10. He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillations", Mech. Res. Commun., 29, 107-111. https://doi.org/10.1016/S0093-6413(02)00237-9
  11. He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A., 374, 2312-2314. https://doi.org/10.1016/j.physleta.2010.03.064
  12. Khavaji, A., Ganji, D.D., Roshan, N., Moheimani, R., Hatami, M. and Hasanpour, A. (2012), "Slope variation effect on large deflection of compliant beam using analytical approach", Struct. Eng. Mech., 44(3), 405-416. https://doi.org/10.12989/sem.2012.44.3.405
  13. Lai ,S.K. and Lim, C.W. (2007), "Nonlinear vibration of a twomass system with nonlinearstiffnesses", Nonlinear Dynam., 49, 233-249. https://doi.org/10.1007/s11071-006-9124-y
  14. Lau, S.L., Cheung, Y.K. and Wu, S.Y. (1983), "Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems", J. Appl. Mech. - ASME, 50(4), 871-876. https://doi.org/10.1115/1.3167160
  15. Masri, S.F. (1972), forced vibration of a class of non-linear twodegree of freedom oscillators", Int. J. Nonlinear Mech., 7, 663-674. https://doi.org/10.1016/0020-7462(72)90006-6
  16. Mehdipour, I., Ganji, D.D. and Mozaffari, M. (2010),. "Application of the energy balance method to nonlinear vibrating equations", Curr. Appl. Phys., 10(1), 104-112. https://doi.org/10.1016/j.cap.2009.05.016
  17. Ozis, T. and Yildirim, A. (2017), "A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity", Chaos Soliton. Fract., 34(3), 989-991. https://doi.org/10.1016/j.chaos.2006.04.013
  18. Oztur, B. and Coskun, S.B. (2011), "The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation'', Struct. Eng. Mech., 37(4), 415-425. https://doi.org/10.12989/sem.2011.37.4.415
  19. Pakar, I. and Bayat, M. (2015), "Nonlinear vibration of stringer shell: An analytical approach", Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 229(1), 44-51. https://doi.org/10.1177/0954408913509090
  20. Sedighi, H.M. and Bozorgmehri, A. (2016), "Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory", Acta Mech., 227(6), 1575-1591. https://doi.org/10.1007/s00707-016-1562-0
  21. Sedighi, H.M., Koochi, A., Daneshmand, F. and Abadyan, M. (2015), "Non-linear dynamic instability of a double-sided nanobridge considering centrifugal force and rarefied gas flow", Int. J. Nonlinear Mech., 77, 96-106 https://doi.org/10.1016/j.ijnonlinmec.2015.08.002
  22. Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133. https://doi.org/10.1016/j.camwa.2009.03.056
  23. Vakakis, A.F. and Rand, R.H. (2004), "Non-linear dynamics of a system of coupled oscillators with essential stifness nonlinearities", Int. J. Nonlinear Mech., 39, 1079 -1091. https://doi.org/10.1016/S0020-7462(03)00098-2
  24. Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108. https://doi.org/10.1016/j.mcm.2011.05.018

피인용 문헌

  1. Structural health monitoring through nonlinear frequency-based approaches for conservative vibratory systems vol.73, pp.3, 2020, https://doi.org/10.12989/sem.2020.73.3.331
  2. A nonlinear stiffness and nonlinear inertial vibration isolator vol.27, pp.11, 2017, https://doi.org/10.1177/1077546320940924
  3. Parameter analyses of suspended cables subjected to simultaneous combination, super and sub-harmonic excitations vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.203