SHAPE AND VIBRATION CONTROL OF SMART STRUCTURE

Abstract

The growing needs of space technology are dictating the use of very large, very light and extremely flexible space structures. For many space applications, a very close tolerance on the shape and surface quality of the structure is essential for their optimal performance. In spite of all the care taken during the manufacturing and deployment, the desired shape and surface accuracy is difficult to achieve. Such accurate shape and surface can be obtained through active control of these structures. Hence, there is a need to develop smart space structures. Many smart space structures such as antenna reflectors are shaped like thin shells. These are made with integrated sensor, actuator and control unit so that any change in the environment may be sensed and the actuators may respond in a manner such that the desired performance of the antenna is maintained. These sensors / actuators are made of piezoelectric material. The sensor and actuators may be bonded to the surfaces of reflectors. Space based antenna reflectors are subjected to shape distortion and vibration due to harsh thermal environment. The sensory and actuation behavior of piezoelectric materials are influenced by the temperature field. Hence the material modeling of piezoelectric material should include piezoelectric effect as well as thermal effects. Before a space structure is flown into space, a thorough understanding of the static and dynamic behavior of these structures must be eveloped. Hence, there is a constant need of development of newer, better and more accurate models of their structural behavior. A critical review of the literature indicates that the static and dynamic behavior of smart layered shells subjected to thermal loading needs to be investigated in greater detail. The present study is aimed at studying the static and dynamic behavior of piezolaminated composite shell structures of various geometries. Since the sensory and actuation behavior ii of piezoelectric materials are influenced by the temperature field, a coupled thermopiezoelectic formulation has been attempted. A finite element formulation is presented for determining the static and dynamic response of coupled thermo-piezo-electric model of a layered shell. The FEM model is based on linear theory of thermo-piezo-electric material. For thin laminated shells, the degenerate shell formulation appears to be the most promising finite element formulation. A degenerate shell element with mechanical, thermal and electric degrees of freedom has been developed in the present work. Sensory and actuation behavior as well as mechanical, electric and thermal loading have been effectively modeled. Using the FEM model, static and dynamic response of piezo-laminated shells have been obtained. To validate the formulation and computer program, the results of the present formulation are compared with existing theoretical and experimental works available in the literature. This study mainly focuses on static shape and vibratory control of various shell geometries, namely singly curved cylindrical shell and doubly curved spherical and paraboloid shells. Some practical problems like shape control of antenna reflector, subjected to thermal loading and beam shaping and beam steering of antenna are investigated. The effect of pyroelectric effect, ie, thermo-piezo-electric coupling on the response of the sensor and actuator has been demonstrated. Effect of therrno-piezo-electric coupling on the deflection of shells has also been studied. The literature review indicates the need for carrying investigations on optimal location of actuators and sensors for static shape control of shell type structures. In view of their practical importance, optimum shape control of paraboloid shell has been investigated through binary-integer —real coded genetic algorithm. iii The vibration control of cylindrical, spherical and paraboloidal shells has been studied using classical controller namely negative velocity feedback controller. In view of their practical importance, optimum placement of actuator / sensor pair for vibration control of paraboloidal shell has been investigated using genetic algorithm. Optimal patch location and corresponding controller gain have been obtained so as to minimize the controller energy. Large space structures (LSS) have highly nonlinear and time-varying structural parameters. Hence, vibration control of these structures using conventional controller is not very effective. Neural network controller has been established as a very valuable tool for vibration control of such smart structures. The vibration control of cylindrical, spherical and paraboloidal shells has been studied using neural network control. The versatility and the effectiveness of the present formulation have been demonstrated through investigations on shape and vibration control of different laminied shell type structures subjected to electro-thermo-mechanical loading.