EFFICIENCY OF PIEZOELECTRIC ENERGY HARVESTING DEVICES UNDER RANDOM VIBRATION CONSIDERING INPUT FREQUENCY CONTENT

This thesis is focused on the analysis of the response of piezoelectric systems for Energy Harvesting subject to ambient natural vibrations. Coherently with what happens in reality, vibrations have been modelled as a random process to represent their variable nature. Moreover, the proper representation of vibrations represents a critical aspect to favor an effective and efficient design of Energy Harvesting devices. In fact, the need for power supply is a critical constraint that sometimes limits the use of such kind of devices in some fields in which they could have an important application. For example, wireless sensors, for which the energy supply, represents a critical aspect not so easy to overcome, unless we accept a dramatic reduction of system affordability and effectiveness. Then, it is clear that maximization of piezoelectric devices energetic efficiency represents an important challenge for their applicability and diffusion. To this aim, in this thesis simple piezoelectric system models for Energy Harvesting, subjected to random vibrations with more realistic representation of frequency, have been studied. So then, differently from what reported in literature, a more sophisticated input model than the Gaussian white noise has been utilized. This last model in fact, albeit simple and effective, does not allow to have a not uniform frequency content of the vibrations. On the contrary, in reality the mechanical vibrations as well as those generated by natural forcing, are often characterized by a specific spectral content, in which the great part of energy is in a specific range of frequency. For this reason, in this thesis, the input has been modelled as a white noise subjected to a linear filtering. This technique allowed to obtain, in term of covariance, the solution for two systems, simple but much representative of piezoelectric devices for Energy Harvesting: namely an electric circuit, with and without, the inductor. In both cases, it has been formally obtained the solution in terms of covariance of the behavior of coupled electro-mechanic system, where the with noise has been colored by two following second order linear filters. The solution has been obtained in general terms both for the stationary and not-stationary case, and has been formulated also in adimensional terms, in order to have a very general calculation tool. Moving from the solution obtained through the Lyapunov’s equations, the mean value of the power generated from the energy harvesting system has been derived, under a specific input. The solution obtained has been then evaluated also in the stationary case for the scheme without the inductor. The quality of the work has been confirmed by the numerical analysis that highlighted that the simplified solution obtained under the hypothesis of a simple white input, is significantly different from the ones obtained in this thesis that uses an input with a specific frequency content. Numerical analysis have been conducted regarding the development of some optimization criteria to be adopted in designing energy harvesting devices. In detail,the optima characteristics of the ratio between natural periods in the mechanical and electric systems coupled has been evaluated, so as to maximize energy yield. Results obtained show that the frequency content influences sensitively both the energetic effectiveness and its optimal value that can be used to present these devices. Finally the study conducted and presented in this thesis, is a clear stimulus for further analysis towards the improvement and the efficiency of these devices by defining new optimization criteria.