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B. Petermeier, H. Ecker:
"Vibration suppression of a cantilever beam by open-loop control of an attached stiffness element";
Talk: 6th EUROMECH Conference ENOC 2008, St. Petersburg; 2008-06-30 - 2008-07-04; in: "Proceedings of the 6th EUROMECH Conference ENOC 2008", (2008), Paper ID 59, 10 pages.

This is a numerical study about new results on the dynamic stability of a beam structure. A uniform cantilever beam with a stiffness element attached to it is investigated. It is assumed that the stiffness parameter of the attached element can be changed periodically with time. Linear and non-linear properties of the stiffness element are considered. The beam structure is discretized by a Finite Element approach. The equations of motion describing the planar vibrations of the beam structure lead to a system with a time-periodic stiffness coefficient. The stability of the linearized system is investigated by a numerical method based on Floquet´s theorem. Numerical simulation is employed to calculate time series of the transient beam deflections for the linear and the non-linear case.
It is demonstrated that suppression of free vibrations can be more effective, if the frequency of the periodic stiffness variation is that of a non-resonant parametric combination resonance frequency. Numerical studies show how the location of the attached stiffness element affects the performance of the proposed method. The assumed moderate non-linearity of the stiffness element has almost no effect on the vibrations of the beam, which confirms the usability of simple electromagnetic devices to realize parametric stiffness excitation.

http://publik.tuwien.ac.at/files/PubDat_170625.pdf