# Vibration performance of a vertical conveyor system under two simultaneous resonances

- 32 Downloads

## Abstract

This study focused on the vibration behavior of a modified vertical conveyor system. The calculated system is exhibited by 2-degree-of-freedom counting quadratic and cubic nonlinearities among both external and parametric forces. Technique of multiple scales connected to gain approximate solutions and study stability of measured structure. All resonances from mathematical solution are extracted. The performance of the system is measured by means of Runge–Kutta fourth-order process (e.g., ode45 in MATLAB). Moreover, two simultaneous resonance cases of this system have been studied analytically and numerically. Stability of acquired numerical solution discovered via frequency response equations. Influences contained by important coefficients scheduled frequency response curves of the considered structure are studied inside numerical results. Methodical results obtained in this work agreed well through the numerical outcome. The description outcome is matched up to available recently published articles.

## Keywords

Vertical conveyor Simultaneous resonances Multiple time scales Vibration behavior Stability## Notes

### Acknowledgements

Authors are really grateful for the comments of referees and suggestion pro-civilizing worth of considered manuscript.

## References

- 1.Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)MATHGoogle Scholar
- 2.Kamel, M., Bauomy, H.S.: Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance. Appl. Math. Model.
**34**, 2763–2777 (2010)MathSciNetCrossRefMATHGoogle Scholar - 3.Nguyen, H.: Simultaneous resonances involving two mode shapes of parametrically- excited rectangular plates. J. Sound Vib.
**332**(20), 5103–5114 (2013)CrossRefGoogle Scholar - 4.Bayıroğlu, H.: Computational dynamic analysis of unbalanced mass of vertical conveyor elevator. In: Sixth International Conference of the Balkan Physical Union. AIP Conference Proceedings, vol. 899, p. 712 (2007)Google Scholar
- 5.Bayıroğlu, H.: Nonlinear analysis of unbalanced mass of vertical conveyor:primary, subharmonic, and superharmonic response. Nonlinear Dyn.
**71**, 93–107 (2013)MathSciNetCrossRefGoogle Scholar - 6.Ding, W.C., Xie, J.H.: Dynamical analysis of a two-parameter family for a vibro-impact system in resonance cases. J. Sound Vib.
**287**, 101–115 (2005)CrossRefGoogle Scholar - 7.Nayfeh, A.H., Mook, D.T., Marshall, L.R.: Nonlinear coupling of pitch and roll modes in ship motion. J. Hydronaut.
**7**, 145–152 (1973)CrossRefGoogle Scholar - 8.Haddow, A.G., Barr, A.D.S., Mook, D.T.: Theoretical and experimental study of modal interaction in a two degree-of-freedom structure. J. Sound Vib.
**97**, 451–473 (1984)MathSciNetCrossRefGoogle Scholar - 9.Balachandran, B., Nayfeh, A.H.: Observations of modal interactions in resonantly forced beam-mass structures. Nonlinear Dyn.
**2**, 77–117 (1991)CrossRefGoogle Scholar - 10.Hegazy, U.H.: Internal-external resonance and saturation phenomenon in a two coupled nonlinear oscillators. Int. J. Mech. Appl.
**4**(3), 101–114 (2014)Google Scholar - 11.Wang, X., Qin, Z.: Nonlinear modal interactions in composite thin-walled beam structures with simultaneous 1:2 internal and 1:1 external resonances. Nonlinear Dyn.
**86**(2), 1381–1405 (2016)CrossRefGoogle Scholar - 12.Saeed, N.A., El-Gohary, H.A.: Influences of time-delays on the performance of a controller based on the saturation phenomenon. Eur. J. Mech. A Solids
**66**, 125–142 (2017)MathSciNetCrossRefGoogle Scholar - 13.Shahgholi, M., Khadem, S.E.: Internal, combinational and sub-harmonic resonances of a nonlinear asymmetrical rotating shaft. Nonlinear Dyn.
**79**, 173–184 (2015)CrossRefGoogle Scholar - 14.Hegazy, U.H.: Single-mode response and control of a hinged-hinged flexible beam. Arch. Appl. Mech.
**79**(4), 335–345 (2009)CrossRefMATHGoogle Scholar - 15.Machado, S.P., Saravia, C.M., Dotti, F.E.: Non-linear oscillations of a thin-walled composite beam with shear deformation. Appl. Math. Model.
**38**, 1523–1533 (2014)MathSciNetCrossRefGoogle Scholar - 16.Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (1993)MATHGoogle Scholar
- 17.Nayfeh, A.H.: Perturbation Methods. Wiley, New York (2000)CrossRefMATHGoogle Scholar