Theoretical modelling of the vibration of plate components of a space structure incorporating piezoelectric actuators is presented. The equations governing the dynamics of the plate, relating the strains in the piezoelectric elements to the strain induced in the system, are derived for isotropic plates using the Rayleigh-Ritz method. The developed model was used for a simply supported plate. The results show that the model can predict natural frequencies of the plate very accurately. Two criteria for the optimal placement of piezoelectric actuators were suggested using modal controllability and the controllability Grammian. The model was then used to predict the closed-loop frequency response of the plate for active vibration control studies with optimal locations of actuators successfully obtained using genetic algorithms. Significant vibration suppression was demonstrated using optimal actuator placement algorithm developed.
The work described in this paper is concerned with controlling the strain of the constraining layer of a composite structure in such a way as to enhance the shear generated in the viscoelastic material and hence improve the overall damping of the composite structure. & ( x ) ith mode shape function CZ displacement function ith damping ratio of the composite beam added damping due to velocity feedback objective function.
It has been shown that significant reductions in structural vibration levels can be achieved using a hybrid system involving constrained layer damping and active control with piezoceramics. In this paper, mathematical models based on the Rayleigh Ritz approach, are developed to describe the longitudinal and flexural vibration behaviour of a cantilevered beam when excited using piezoceramic patches bonded to a constrained layer damping treatment. Predictions of static and steady state dynamic behaviour, obtained using the models are validated by comparison with results from finite element analysis and laboratory experiments. The models are then used in open loop and closed loop velocity feedback control simulations to demonstrate the improvements in stability and performance achieved using this method over that achieved using conventional active control.
Theoretical modelling of active flutter suppression of plate components of a
aerospace structure is presented. The equations governing the dynamics of the
panel, relating the strains in the piezoelectric elements to the strain induced in
the system, are derived for isotropic plates using the Rayleigh–Ritz method. A
criterion for optimal placement of piezoelectric actuators was suggested using
modal controllability. The model was then used to find the optimal location for
the piezoelectric actuator utilizing genetic algorithms. The linear quadratic
Gaussian design method was used to stabilize the panel flutter using a
piezoelectric actuator. This study clearly showed that the flutter can be delayed
using the piezoelectric actuator.
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