Slow high-frequency effects in mechanics: problems, solutions, potentials

Jon Juel Thomsen (Invited author)

Research output: Contribution to journalConference articleResearchpeer-review

Abstract

Strong high-frequency excitation (HFE) may change the ‘slow’ (i.e. effective or average) properties of mechanical systems, e.g. their stiffness, natural frequencies, equilibriums, equilibrium stability, and bifurcation paths. This tutorial describes three general HFE effects: Stiffening – an apparent change in the stiffness associated with an equilibrium; Biasing – a tendency for a system to move towards a particular state which does not exist or is unstable without HFE; and Smoothening – a tendency for discontinuities to be apparently smeared out by HFE. The effects and a method for analyzing them are introduced first in terms of simple physical examples, and then in generalized form for mathematical models covering broad classes of discrete and continuous mechanical systems. Several application examples are summarized. Three mathematical tools for analyzing HFE effects are described and compared: The Method of Direct Separation of Motions, the Method of Averaging, and the Method of Multiple Scales. The tutorial concludes by suggesting that more vibration experts, researchers and students should know about HFE effects, for the benefit not only of general vibration troubleshooting, but also for furthering the creation of innovative technical devices and processes utilizing HFE effects.
Original languageEnglish
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume15
Issue number9
Pages (from-to)2799–2818
ISSN0218-1274
DOIs
Publication statusPublished - 2005
Event5th EUROMECH Nonlinear Dynamics Conference - Eindhoven, Netherlands
Duration: 7 Aug 200512 Aug 2005
Conference number: 5

Conference

Conference5th EUROMECH Nonlinear Dynamics Conference
Number5
CountryNetherlands
CityEindhoven
Period07/08/200512/08/2005

Keywords

  • High-frequency excitation
  • Fast vibrations
  • Direct separation of motions
  • Stiffening
  • Biasing
  • Smoothening
  • Vibrational control

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