7 Special Effects
of High-Frequency Excitation
7.1 Introduction
What happens with a system being excited at a very high frequency, far beyond the
highest underdamped natural frequency? You might think it simply responds at a
similar high frequency in a trivial manner, since resonance effects are not at play.
Indeed, vibration experts are typically trained to neglect possible high-frequency
(HF) components of excitations. This often makes sense, since mechanical systems
are lowpass filters, with a frequency response quickly vanishing beyond the highest
subcritically damped natural frequency.
But probably you already know what happens with a simple pendulum, whose
support is vibrated vertically at small amplitude and a frequency much higher than
the fundamental natural frequency: The pendulum stabilizes in its upside-down
position (a phenomenon we shall dwell further into below). This is a classic
example of a ‘slow’ (in the sense ‘average’) effect of HF excitation, lasting as long
as the HF excitation is sufficiently energetic. Other examples include changing dry
friction into apparent viscous damping; transportation of mass (e.g. solid bodies,
granular material, or fluids), and apparent changes in system stiffness, natural frequency, stability, and equilibriums.
Even a small-amplitude symmetric HF excitation may feed off significant
asymmetric effects, and cause drastic changes to the low-frequency properties of a
system. The effects may be interesting or strange, useful or disturbing, dangerous or
disastrous – dependent on the circumstances. Or even be unimportant in many
cases, but one cannot know without being capable of predicting and analyzing
them.
Mechanical HF excitation provides the working principle behind many industrial
applications, e.g., transport of material on vibration feeders, auto focusing of
camera lenses, submersion of piles, or separation of solid materials according to
size or density (e.g. Blekhman 2000; Blekhman and Sorokin 2016; Sorokin et al.
2010; Cabboi et al. 2020). In the context of dynamic materials (Lurie 2007),
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. J. Thomsen, Vibrations and Stability,
https://doi.org/10.1007/978-3-030-68045-9_7
387
of High-Frequency Excitation
7.1 Introduction
What happens with a system being excited at a very high frequency, far beyond the
highest underdamped natural frequency? You might think it simply responds at a
similar high frequency in a trivial manner, since resonance effects are not at play.
Indeed, vibration experts are typically trained to neglect possible high-frequency
(HF) components of excitations. This often makes sense, since mechanical systems
are lowpass filters, with a frequency response quickly vanishing beyond the highest
subcritically damped natural frequency.
But probably you already know what happens with a simple pendulum, whose
support is vibrated vertically at small amplitude and a frequency much higher than
the fundamental natural frequency: The pendulum stabilizes in its upside-down
position (a phenomenon we shall dwell further into below). This is a classic
example of a ‘slow’ (in the sense ‘average’) effect of HF excitation, lasting as long
as the HF excitation is sufficiently energetic. Other examples include changing dry
friction into apparent viscous damping; transportation of mass (e.g. solid bodies,
granular material, or fluids), and apparent changes in system stiffness, natural frequency, stability, and equilibriums.
Even a small-amplitude symmetric HF excitation may feed off significant
asymmetric effects, and cause drastic changes to the low-frequency properties of a
system. The effects may be interesting or strange, useful or disturbing, dangerous or
disastrous – dependent on the circumstances. Or even be unimportant in many
cases, but one cannot know without being capable of predicting and analyzing
them.
Mechanical HF excitation provides the working principle behind many industrial
applications, e.g., transport of material on vibration feeders, auto focusing of
camera lenses, submersion of piles, or separation of solid materials according to
size or density (e.g. Blekhman 2000; Blekhman and Sorokin 2016; Sorokin et al.
2010; Cabboi et al. 2020). In the context of dynamic materials (Lurie 2007),
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. J. Thomsen, Vibrations and Stability,
https://doi.org/10.1007/978-3-030-68045-9_7
387