A modal dynamic model was developed for the active vibration control of laminated doubly curved shells with piezoelectric sensors and actuators. The dynamic effects of the mass and stiffness of the piezoelectric patches were considered in the model. Finite element equations of motion were developed based on shear deformation theory and implemented for an isoparametric shell element. The mode superposition method was used to transform the coupled finite element equations into a set of uncoupled equations in the modal coordinates. A robust controller was developed using Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) design methodology to calculate the gain and actuator voltage requirements. A Neural Network controller was then designed and trained offline to emulate the performance of the LQG/LTR controller. Numerical results have been presented for a flat plate and a spherical shell showing the variation in initial conditions and structural parameters. The neural network controller was shown to effectively emulate the LQG/LTR controller.

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A neural network-based control system is developed for self-adapting vibration control of laminated plates with piezoelectric sensors and actuators. The conventional vibration control approaches are limited by the requirement of an explicit and often accurate identification of the system dynamics and subsequent 'offline' design of an optimal controller. The present study utilizes the powerful learning capabilities of neural networks to capture the structural dynamics and to evolve optimal control dynamics. A hybrid control system developed in this paper is comprised of a feed-forward neural network identifier and a dynamic diagonal recurrent neural network controller. Sensing and actuation are achieved using piezoelectric sensors and actuators. The performance of the hybrid control system is tested by numerical simulation of a composite plate with embedded piezoelectric actuators and sensors. Finite-element equations of motion are developed based on shear deformation theory and implemented for the plate element. The dynamic effects of the mass and stiffness of the piezoelectric patches are considered in the model. Numerical results are presented for a flat plate. A robustness study including the effects of structural parameter variation and partial loss of the sensor and actuator is performed. The hybrid control system is shown to perform effectively in all of these cases.

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