The static responses and displacement control of circular curved beams with piezoelectricactuators

Abstract

We analyse the static responses of a circular curved beam bonded with a singlepiezoelectric actuator or symmetric actuators. We also study the characteristics of thecontrol parameters for the displacement control of a cantilever circular curved beamvia piezoelectric actuators in this paper. The uniform circular beam is thin andactuated by thin piezoelectric layers. The piezoelectric unimorph or the bimorphbeam is equivalent to a single-layer structure. The governing equations of thesestructures with small curvature are derived based on one-dimensional beam theory.The static analysis of the segmented beam undergoing radial concentrated loadand concentrated bending moment is given in detail. For a cantilever beam withsingle actuator or symmetric actuators, the theoretical results of the displacementresponses agree well with experimental results reported early and/or the FEM results.The control problem of a cantilever bimorph is studied as the first example. Tocontrol the displacement at the free end by piezoelectric actuation, an explicitexpression of the optimal voltage is obtained for the beam undergoing the radialconcentrated load at an arbitrary location, which indicates the optimal voltage isindependent of the material properties of the middle elastic layer. Numerical resultsshow that the peak control voltage and the negative control voltage will occurwith the changes of the load location and the beam length. The cantilever beamwith symmetric distributed actuators is studied as the second example. As thebeam is loaded by too high a radial concentrated load at the free end, the radialdisplacement of the free end is controlled to the minimum via actuators withgiven input voltage. The optimization of the actuators’ length and location isimplemented. For a given actuator’s length, the optimal actuator’s location is at theclamped end as the central angle of the beam is smaller than a critical value.After the central angle of the beam is larger than the critical value, the optimalvalue of the actuator’s location is dependent on the central angle of the beamand the central angle of the actuators. As the actuator’s location is given, theoptimal length of the actuators is the allowable maximum length of the actuators.