Abstract
In this paper, a formulation of a sandwich plate integrating an elastic central layer (isotropic or composite) between two piezoelectric sub-layers (actuators and/or sensors), which can be taken as a smart (intelligent) structure and allowing active control vibrations is presented. A 9-node finite element quadratic plate element with 5 degrees of freedom per node is used which takes into account the effect of transverse shear with an additional degree of freedom for each node of the piezoelectric sub-layer. At First, the static control of the deflection by taking the two piezoelectric sub-layers as actuators with two configurations of the total and partial recovery of the surface is undertaken. Thus, the influence of patches position, for the second configuration, on the attenuation of vibrations is analyzed. In a Second step, the active vibration control using two types of LQR and PID controllers with different control parameters is tested and compared for the two recovery configurations (total and partial) of the piezoelectric elements. It is demonstrated throughout the present results that the performances of the partial recovery are almost as good as those of the total recovery despite a ratio of the surfaces piezoelectric patches which is 1/3. It is also noticed that the PID controller is more efficient than the LQR controller. But, if using the PSO (Particle Swarm Optimization) algorithm, the LQR's parameters are optimized and give almost the same performances as those of the PID controller.DOI: http://dx.doi.org/10.5755/j01.mech.24.5.20645
Highlights
The piezoelectricity is used to control the dynamic behavior of structures in order to attenuating vibrations, avoid the resonance and the damage at a later
[5] Hwang et al presented a finite element formulation for vibration control of a laminated plate with piezoelectric sensors/actuators, and for a laminated plate under the negative velocity feedback control, the direct time responses are calculated by the Newmark-β method, and the damped frequencies and modal damping ratios are derived by modal state space analysis
A finite element method based on the classical laminated plate theory is developed for the active vibration control of a composite plate containing distributed piezoelectric sensors and actuators by Lam et al [6], and the static analysis and active vibration suppression of a cantilever composite plate are performed as a numerical example to verify the proposed model
Summary
The piezoelectricity is used to control the dynamic behavior of structures in order to attenuating vibrations, avoid the resonance and the damage at a later. Dimitradis et al [3] studied the behavior of two dimensional patches of piezoelectric material bonded to the surface of elastic distributed structures and used as vibration actuators is analytically investigated, and the theory is applied to develop an approximate dynamic model for the vibration response of a supported elastic rectangular plate. A finite element method based on the classical laminated plate theory is developed for the active vibration control of a composite plate containing distributed piezoelectric sensors and actuators by Lam et al [6], and the static analysis and active vibration suppression of a cantilever composite plate are performed as a numerical example to verify the proposed model. A static deflection control of clamped composite plate by applying various voltages on the actuators is undertaken, and the active control analysis using LQR and PID controllers for attenuating free and forced vibrations has been studied and compared as well
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