Abstract
SummaryThis contribution presents novel results on feed‐forward control of stress in piezoelectric structures by means of piezoelectric actuation. For that sake, we focus on a one‐dimensional benchmark problem, a piezoelectric transducer that is excited by a piezoelectric stack actuator. We investigate the following problem: Is it possible to actuate the piezoelectric transducer in such a manner that the dominant axial stress component is nullified. In order to find a theoretical solution for this question, we discretize our system as a two‐degree‐of‐freedom (2DOF) model. The equations of motion are transformed into the differential equations for the inner forces by taking advantage of the constitutive relations, which relate displacement, stress, and electric field. Finally, we find a mathematical relation for the piezoelectric transducer excitation in order to annihilate the transducer force. A static and a frequency‐dependent approximate solution for the transducer actuation signal are derived. The latter solution reduces the inner force drastically in a certain frequency range. After numerical results for the force‐control algorithm are presented, we finally experimentally verify our theory: First, the force‐controlled configuration is exposed to a monofrequent harmonic excitation test run for 30 min, showing no sign of fatigue or material failure, because the transducer force is below the ultimate tensile strength. Then, the system is excited by the same harmonic excitation again, but the control signal for the piezoelectric transducer is turned off. The result is a visible damage of the piezoelectric transducer, leading to a significant change of the first eigenfrequency.
Highlights
Smart or intelligent structures are equipped with multifunctional materials
The experimental setup eventually verifies our proposed stress control method: We show that the piezoelectric transducer, as long as the theoretically derived piezoelectric actuation signal for stress control is applied, remains undamaged during a 30‐min test run
We weighed the masses of the stack, the transducer, and the attached mass and used the stiffness values and the piezoelectric coefficients from the manufactHuvTrAerð'ωs Þd1⁄4atGasvThAees1⁄4t j ωinanadfiHrsvTtTsðtωeÞp.1⁄4TGhvTeTn,s1⁄4ijnω a later step, we of the simulation compared results to the frequency response functions (FRFs) the experimental ones
Summary
Smart or intelligent structures are equipped with multifunctional materials. These structures often take advantage of the piezoelectric effect in order to track the displacement of a flexible system. Shape control and displacement tracking are feed‐forward control methods, where one asks for the control actuation in order that a certain desired displacement field is obtained. In case of piezoelectric control elements, one asks for the actuating electric field and its spatial distribution. The influence of the much smaller direct piezoelectric effect, which is frequently exploited in structural health monitoring for the sake of measuring structural displacements, is usually neglected, or it is taken into account in an approximate manner in the actuation context. The direct piezoelectric effect is needed for automatic control algorithms, which are not in the focus of the present contribution but which should be superimposed when the above assumptions for successful feed‐forward control are not satisfied in a sufficient manner
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