Abstract
Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton’s principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG-Kalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.
Highlights
In the piezoelectric sensors applications, mechanically or thermally induced deformations can be determined from measurement of the induced electrical potential, whereas in piezoelectric actuator applications deformation of strain can be controlled through the introduction of appropriate electric potential
We show that the control procedure cannot be perturbed by applying a thermal gradient and the control can be applied at any time during the period of vibration of the plate
The study consists of three phases; the first is to verify the actuation in the static case by exciting the actuator by constant and harmonic inputs; the second phase corresponds to analyse the responses of the structure dynamics under a center plate pulse and study the effect of the location of piezoelectric elements on the effectiveness of control; and the third phase was dedicated to analyzing the effect of thermoelastic and pyroelectric coupling, by applying thermal gradient, on the dynamics of the structure and the control procedure
Summary
In the piezoelectric sensors applications, mechanically or thermally induced deformations can be determined from measurement of the induced electrical potential, whereas in piezoelectric actuator applications deformation of strain can be controlled through the introduction of appropriate electric potential. By integrating distributed piezoelectric sensors/actuators and advanced composites, the potential exists for forming high-strength, high stiffness, lightweight structures capable of self-monitoring and self-controlling. Typical applications of such structures are envisioned in the thermal distortion management of propulsion components and space structures. Thermal effects become important when the piezoelectric structure has to operate in either extremely hot or cold temperature environments These extreme conditions may severely affect the response of piezoelectric elements by induction of thermal stresses resulting from thermoelastic and pyroelectric coefficients. De Abreu et al [3] have implemented finite element modeling of a plate with localized piezoelectric sensors and actuators. We show that the control procedure cannot be perturbed by applying a thermal gradient and the control can be applied at any time during the period of vibration of the plate
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