Jürgen Schöftner, Gerda Buchberger, Hans Irschik,
"Static and dynamic shape control of slender beams by piezoelectric actuation and resistive electrodes"
, in Composite Structures, Vol. 111, Seite(n) 66-74, 2014, ISSN: 1879-1085
Original Titel:
Static and dynamic shape control of slender beams by piezoelectric actuation and resistive electrodes
Sprache des Titels:
Englisch
Original Kurzfassung:
In the present paper a concept of static and dynamic shape control for slender piezoelastic beams is
addressed. The notion shape control means to find a weighting sequence for the piezoelectric control
units, such that force-induced lateral deflections are completely annihilated along the beam axis. In
our case this spatial control intensity for the piezoelectric transducers is realized with so-called resistive
electrodes: by prescribing only the maximum and minimum voltage level, any desirable voltage distribution
along the beam axis may be obtained. For the derivation of the shape control method an extended
version of the Bernoulli?Euler beam theory is used, which unifies the kinematics of a slender piezoelectric
beam and the Telegrapher?s equations for moderately conductive electrodes. The outcome is an actuator
equation for the displacement, which is fourth order in space and second order in time, and a sensor
equation, which is second order in space and first order in time (diffusion equation for the voltage). The
developed shape control method is verified by several numerical examples in the static case as well as in
the dynamic frequency regime for a clamped-free beam. We show that the presented method is perfectly
suited for static loads, being able to cancel force-induced structural deformations along the beam axis,
whereas the deflections in the higher frequency regime can be nearly canceled out. The method is efficient,
as long as a non-dimensional constant, involving the resistance, the capacitance per unit length,
the length of the electrodes and the excitation frequency, is small.