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T. Pumhössel, H. Ecker:
"Active damping of vibrations of a cantilever beam by axial force control";
in: "Proceedings 2007 ASME International Design Engineering Technical Conferences", ASME, 2007, ISBN: 0-7918-3806-4, Paper ID DETC2007-34638, 11 pages.

In several fields, e.g. aerospace applications, robotics or the
bladings of turbomachinery, the active damping of vibrations of
slender beams which are subject to free bending vibrations becomes
more and more important.
In this contribution a slender cantilever beam loaded with a
controlled force at its tip, which always points to the clamping
point of the beam, is treated. The equations of motion are obtained
using the Bernoulli-Euler beam theory and d´Alemberts
principle. To introduce artificial damping to the lateral vibrations
of the beam, the force at the tip of the beam has to be controlled in
a proper way. Two different methods are compared. One concept
is the closed-loop control of the force. In this case a nonlinear
feedback control law is used, based on axial velocity feedback of
the tip of the beam and a state-dependent amplification. By contrast,
the concept of open-loop parametric control works without
any feedback of the actual vibrations of the mechanical structure.
This approach applies the force as harmonic function of
time with constant amplitude and frequency. Numerical results
are carried out to compare and to demonstrate the effectiveness
of both methods.

Project Head Horst Ecker:
Schwingungsunterdrückung durch Parametererregung