Finite Element Based Design and optimal Vibration Control of Smart fiber Reinforced composite shell structures using genetic algorithm
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Active vibration control of smart fiber reinforced polymer (FRP) composite structures finds use in high performance structures especially in lightweight composite structures. Proper implementation of such smart structure systems demands complete understanding of their responses and design of an appropriate control system. The present work deals with first development of an improved shell finite element (FE) formulation for coupled thermo-electromechanical analysis of smart FRP shell structures followed by development of genetic algorithm (GA) based methodologies for optimal actuators placement as well as optimal feedback controller. Stress resultant-type KoiterDs shell theory has been used and no restriction has been imposed on the magnitude of curvature components to capture the deep and shallow shell cases. The twist curvature component has been incorporated along with the normal curvatures to keep the strain equations complete. The transverse shear effect has also been considered according to the MindlinDs hypothesis. An improved integer coded genetic algorithm (GA) based open loop procedure has been implemented for optimal placement of collocated sensors and actuators in order to maximize the controllability index incorporating control spillover. Once, the optimal sensor/actuator locations have been obtained, an improved real coded GA based linear quadratic regulator (LQR) control scheme has been developed for optimal vibration control of the smart shell structures under combined thermo-mechanical loading in order to maximize the closed loop damping ratio while keeping actuators voltages within limit. The FE formulations developed in the present work has been compared with analytical solutions for smart shell structures subjected to electrical, mechanical, thermal as well as combined electro-thermo-mechanical loading. It is observed that the developed FE could analyze coupled thermo-electro-mechanical of shell structures for both deep and shallow shells. Results obtained from the present work also show that this combined GA based optimal sensor/actuator placement and GA based LQR control scheme is far superior to conventional active vibration control using LQR control schemes. It is observed that the proposed GA based LQR control scheme along with the optimal placement of actuators could control both the dynamic oscillation due to mechanical load as well as the static displacement due to thermal gradient which was not possible with conventional LQR control scheme. The proposed GA based combined optimal placement and LQR control scheme not only lead to increased closed loop damping ratio but also shows a drastic reduction in input/actuation voltage..
Supervisor: Debabrata Chakroborty