Abstract
This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.
Similar content being viewed by others
References
Hartog, J. P. den, Mechanical Vibrations, McGraw-Hill, 1956.
Hunt, J. B., Dynamic Vibration Absorbers, London: Mechanical Engineering Publications, 1979.
Korenev, B. G. and Reznikov, L. M., Dynamic Vibration Absorbers, Wiley, 1993.
Shaw, S. W. and Holmes, P. J., 'A periodically forced piecewise linear oscillator', Journal of Sound and Vibration 90(1), 1983, 129–155.
Thompson, J. M. T., Bokaian, A. R., and Ghaffari, R., 'Subharmonic resonances and chaotic motions of a bilinear oscillator', Journal of Applied Mathematics 31, 1983, 207–234.
Natsiavas, S., 'On the dynamics of oscillators with bi-linear damping and stiffness', International Journal of Non-Linear Mechanics 25(5), 1990, 535–554.
Fey, R. H. B., 'Steady-State Behaviour of Reduced Dynamics with Local Nonlinearities', Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 1992.
Vorst, E. L. B. van de, 'Long Term Dynamics and Stabilization of Nonlinear Mechanical Systems', Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 1996.
Pun, D. and Liu, Y. B., 'On the design of the piecewise linear vibration absorber', Nonlinear Dynamics 22, 2000, 393–413.
Fey, R. H. B. and van Liempt, F. P. H., 'Sine sweep and steady-state response of simplified solar array models with nonlinear elements', in Proceedings of the International Conference on Structural Dynamics Modelling; Test, Analysis, Correlation and Validation, Vols. 201-210, N. M. M. Maia, J. M. Montalvao e Silva, and A. M. Relogio Ribeiro (eds.), Funchal, Madeira, Portugal, 2002.
Rubin, S., 'Improved component-mode representation for structural dynamic analysis', AIAA Journal 13(8), 1975, 995–1006.
Newhouse, S., Ruelle, D., and Takens, F. 'Occurrence of strange axiom-a attractors near quasi periodic flow on T m, m ? 3', Communication Mathematical Physics 64, 1978, 35–40.
Grebogi, C., E. Ott, and Yorke, J. A., 'Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems?', Physical Review Letters 51, 1983, 339–342.
Pazo, D., Sanchez, E., and Matias, M. A., 'Transition to high-dimensional chaos through quasiperiodic motion', International Journal of Bifurcation and Chaos 10, 2001, 2683–2688.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., 'Determining Lyapunov exponents from a time series', Physica 16D, 1985, 285–317.
Hegger, R., H. Kantz, and Schreiber, T., 'Practical implementation of nonlinear time series methods: The TISEAN package', Chaos 9, 1999, 413–435.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bonsel, J.H., Fey, R.H.B. & Nijmeijer, H. Application of a Dynamic Vibration Absorber to a Piecewise Linear Beam System. Nonlinear Dynamics 37, 227–243 (2004). https://doi.org/10.1023/B:NODY.0000044646.70030.31
Issue Date:
DOI: https://doi.org/10.1023/B:NODY.0000044646.70030.31