Abstract
High frequency excitation affects the ‘slow’ linear behavior of a dynamical system: equilibria may move and disappear, gain or lose stability. An appearance of the ‘vibrational force’, which accounts for the effect of the fast excitation, also changes nonlinear properties of the system. These effects are considered and analyzed in the present study.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kapitza, P. L.: Dynamic stability of a pendulum with an oscillating point of suspension (in Russian), Zumal Eksperimental’noj i Teoreticeskoj Fiziki 21(5) (1951), 588–597.
Chelomei, V. N.: Mechanical paradoxes caused by vibrations, Soviet Physics Doklady 28(5) (1983), 387–390.
Kolovskij, M.Z.: Influence of fast-frequency excitation to resonant oscillations in nonlinear systems (in Russian), Trudy Leningradskogo Politehniceskogo Instituta 226 (1963), 7–17.
Blekhman, I. I.: Vibrational Mechanics, Fizmatlit Publishing Company, Moscow, 1994. (In Russian; To appear in English translation by World Scientific Publishing Company, 1998 or later).
Tchemiak, D.M., Thomsen, J.J.: Slow effects of fast harmonic excitation for elastic structures, (to appear in Nonlinear Dynamics).
Thomsen, J. J.: Using perturbation methods to study slow effects of fast, non-resonant excitation, DCAMM Report (to appear), Technical University of Denmark.
Schmitt, J.M., Bayly, P.V.: Bifurcations in the mean angle of a horizontally shaken pendulum: analysis and experiment, Nonlinear Dynamics 15 (1998), 1–14.
Jensen, J. S.: Nonlinear dynamics of the follower-loaded double pendulum with added support-excitation, (Journal of Sound and Vibration, in press).
Jensen, J. S.: Pipes conveying fluid pulsating with high frequency, DCAMM Report No. 563, Technical University of Denmark, 1998.
Thomsen, J.J.: Vibration-induced displacement using high-frequency resonators and friction layers, in Proceedings of the IUTAM/IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems — SNDS’98, September 24–28,1998, Riga, Latvia.
Tchemiak, D.M.: The influence and utilization of fast excitation on a continuous system, DCAMM Report (to appear), Technical University of Denmark.
Thomsen, J. J.: Vibrations and Stability, Order and Chaos, McGraw-Hill, London, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Tcherniak, D.M. (2000). Using Fast Vibration to Change the Nonlinear Properties of Mechanical Systems. In: Lavendelis, E., Zakrzhevsky, M. (eds) IUTAM / IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems. Solid Mechanics and its Applications, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4229-8_24
Download citation
DOI: https://doi.org/10.1007/978-94-011-4229-8_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5836-0
Online ISBN: 978-94-011-4229-8
eBook Packages: Springer Book Archive