Piezoelectric materials are characterized by two well known different effects, the direct and the converse one. The former effect, that is the property of converting vibrations into electrical energy, is studied in the field of Energy Harvesting (EH) in order to produce not expensive and non-polluting energy by making use of natural vibrations. In the last two decades this aspect has been object of interesting research widely. The latter effect consists of producing strain on a material subjected to electrical polarization. For this reason it can be exploited to design piezoelectric transducers. In this chapter it is shown that both the above mentioned situations can be analyzed basing on the piezoelectric constitutive equations, proposed by IEEE Standard on Piezoelectricity. The study is carried out by characterizing the constitutive matrices for the piezoelectric material in testing and implementing the equations of the mathematical model by a software that uses the Finite Element Method (FEM). This model allows to choose the fitting piezoelectric material in each of the previous situation and its best geometrical and physical properties like length, width, height, weight, position. In the last paragraph a nondestructive diagnosis is performed by the simulations of a device for ultrasonic probes and a thin structure useful for Energy Harvesting is presented.
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