Many of energy harvesting devices use piezoelectric elements to convert mechanical vibrations into usable electrical energy. The input excitation is usually assumed to be a deterministic harmonic wave, while in practical situations, the mechanical excitation of the media is a random signal. So, the objective of this research is to study the energy harvesting in piezoelectric devices using the random vibration theory. At the first step a lumped parameter physical model of the device is presented. A mathematical model is then developed by obtaining the normalized differential equations governing the voltage induced in the energy harvesting circuit as well as the length of the piezoelectric material. The random vibration theory is then utilized to derive analytical expressions for the statistical properties of the voltage, power and the length of the piezoelectric material in terms of the statistical properties of the excitation which is assumed to be a band limited white noise. It is shown that with proper selection of the system parameters, the expected value of the harvested power can be effectively maximized. The qualitative and quantitative knowledge resulting from this effort is expected to enable the analysis, optimization, and synthesis of piezoelectric energy harvesting devices.

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