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

摘要

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 with a suggestion that more vibration experts, researchers and students should be aware of HFE effects, for the benefit of general vibration troubleshooting, and also for furthering the creation of innovative technical devices and processes utilizing HFE effects.