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Tuning inertial nonlinearity for passive nonlinear vibration control

  • Samuel C. StantonEmail author
  • Dean Culver
  • Brian P. Mann
Original paper
  • 40 Downloads

Abstract

This paper examines the viability of completely passive control approach based on multiple timescale perturbation methods to elicit desired dynamic cancellation or suppression of nonlinear vibration characteristics. Without appeal to feedback, auxiliary oscillating systems, or nonlinear energy sinks, we demonstrate how inertial nonlinearity balancing can more simply realize distortion-free vibrational responses that are robust to very strong forcing amplitudes across resonant, super-harmonic, and sub-harmonic excitation frequencies as well as opportunities to passively suppress hysteresis, cusp-fold bifurcations, and higher harmonics. Of particular merit are the variegated results concerning critical design points for passive control of sub-harmonic resonances. To most simply capture the essence and broad relevance of the approach, we focus upon a variant of the Duffing oscillator that describes moderately large amplitude vibration of a cantilever beam, various link systems, and kinematically constrained particle motion. The results herein are anticipated to be the most relevant to NEMS/MEMS- based sensing research and technology as well as vibration-based mechanical energy harvesting or mechanical filtering.

Keywords

Inertial nonlinearity Method of multiple scales Passive vibration control Mechanical filter 

Notes

Acknowledgements

The views expressed are those of the writer and not the Army, DoD, or its components. This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/Grant Number W911NF-12-R-0012-04.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

No animals or human subjects were used during the course of the research.

References

  1. 1.
    Wang, X., Xu, L., Fu, P., Li, J., Wu, Y.: Harmonics analysis of the iter poloidal field converter based on a piecewise method. Plasma Sci. Technol. 19, 1–8 (2017)Google Scholar
  2. 2.
    Xu, X., Collin, A., Djokic, S., et al.: Operating cycle performance, lost periodicity, and waveform distortion of switch-mode power supplies. IEEE Trans. Instrum. Meas. 67, 2434–2443 (2018)CrossRefGoogle Scholar
  3. 3.
    Singh, G.: Power systems harmonics research: a study. Eur. Trans. Electr. Power 19, 151–172 (2009)CrossRefGoogle Scholar
  4. 4.
    Omidi, E., Mahmoodi, S.: Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach. Nonlinear Dyn. 79, 835–849 (2015)CrossRefGoogle Scholar
  5. 5.
    Jalili, M., Dadfarnia, D., Dawson, D.: A fresh insight into the microcantilever-sample interaction problem in non-contact atomic force microscopy. J. Dyn. Syst. Meas. Control 126, 327–335 (2004)CrossRefGoogle Scholar
  6. 6.
    Librescu, L., Marzocca, P.: Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mech. 178, 147–186 (2005)CrossRefGoogle Scholar
  7. 7.
    Gao, J., Shen, Y.: Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators. J. Sound Vib. 264, 911–928 (2003)CrossRefGoogle Scholar
  8. 8.
    Liu, C., Jing, X., Daley, S., Li, F.: Recent advances in micro-vibration isolation. Mech. Syst. Signals Process. 56–57, 55–80 (2015)CrossRefGoogle Scholar
  9. 9.
    Lee, Y., Vakakis, A., Bergman, L., McFarland, D., Kerschen, G., Nucera, F., Tsakirtzis, S., Panagopoulos, P.: Passive non-linear targeted energy transfer and its applications to vibration absorption: a review. Proc. IMechE 222, 77–134 (2008)CrossRefGoogle Scholar
  10. 10.
    Pennisi, G., Mann, B., Naclerio, N., Stephan, C., Michon, G.: Design and experimental study of a nonlinear energy sink coupled to an electromagnetic energy harvester. J. Sound Vib. 437, 340–357 (2018)CrossRefGoogle Scholar
  11. 11.
    Gendelman, O., Manevitch, L., Vakakis, A., M’Closkey, R.: Energy pumping in nonlinear mechanical oscillators: Part i—dynamics of the underlying hamiltonian system. J. Appl. Mech. 68, 34–41 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Marinca, V., Herianu, N.: Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method. J. Sound Vib. 329, 1450–1459 (2010)CrossRefGoogle Scholar
  13. 13.
    Bayat, M., Pakar, I., Cveticanin, L.: Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: an analytical approach. Mech. Mach. Theory 77, 50–58 (2014)CrossRefGoogle Scholar
  14. 14.
    McHugh, K., Dowell, E.: Nonlinear responses of inextensible cantilever and free?free beams undergoing large deflections. J. Appl. Mech. 85, 1–8 (2018)CrossRefGoogle Scholar
  15. 15.
    Villanueva, L.G., Karabalin, R.B., Matheny, M.H., Chi, D., Sader, J.E., Roukes, M.L.: Nonlinearity in nanomechanical cantilevers. Phys. Rev. B 87, 024304 (2013)CrossRefGoogle Scholar
  16. 16.
    Nayfeh, A., Mook, D.: Nonlinear Oscillations, 2nd edn. Wiley, Hoboken (1978)zbMATHGoogle Scholar
  17. 17.
    Culver, D., Mann, B., Stanton, S.: Passive subharmonic elimination. Appl. Phys. Lett. 113, 1–3 (2018)CrossRefGoogle Scholar

Copyright information

© US Government 2019

Authors and Affiliations

  1. 1.Engineering Sciences DirectorateUS Army Research OfficeAdelphiUSA
  2. 2.Vehicle Technology DirectorateUS Army Research LaboratoryAdelphiUSA
  3. 3.Mechanical Engineering and Material Science DepartmentDuke UniversityDurhamUSA

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