Modeling and shape estimation of smart structures for active control

Piezoelectric materials allow the transformation of electric constraints into mechanical constraints and vice versa. They are used as controllers or sensors in the industrial field. The analysis of the behavior of piezoelectric materials lays within the use of these materials in structures whose form or modes of vibration are to be controlled. The need for these studies is crucial. From a general point of view, the need for stability of structures has become increasingly important with the development of technologies related to telecommunications and microtechniques. Adaptive structures are the only means to achieve the requisite stability in the face of diverse situations. The objective of this research is to model the effect of electro- mechanical coupling and to estimate the shape of the adaptive structures for active control. Ideal models were developed for various adaptive structures. These models make it possible to determine the static and dynamic behavior of these structures. The model behavior was compared with experimental results and the, numerical, finite elements and the Rayleigh-Ritz methods. Results obtained from all of the above approaches reveal good agreements among them. For a possible application of active control, the analysis of substructures in commercial FEA software ANSYS is used to extract the mass, the rigidity and input matrices. In order to evaluate at real time the shape of the flexible or composite structures, an algorithm was developed to determine the forms of the structures under arbitrary loads and different boundary conditions. The results obtained by this method were compared with those obtained from numerical, the finite elements and experimental methods. The results also, show that the developed algorithm makes it possible to correctly estimate the structures.

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