Dynamic Modeling and Neural Control of Composite Shells Using Piezoelectric Devices

Abstract

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.