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

Jon Juel Thomsen (Invited author)

    Research output: Contribution to journalConference articleResearchpeer-review


    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
    Issue number9
    Pages (from-to)2799–2818
    Publication statusPublished - 2005
    Event5th EUROMECH Nonlinear Dynamics Conference - Eindhoven, Netherlands
    Duration: 7 Aug 200512 Aug 2005
    Conference number: 5


    Conference5th EUROMECH Nonlinear Dynamics Conference


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


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