Vibrational piezoelectric harvesting devices (PHD) provide an autonomous power source for various types of sensors, actuators and MEMS devices. There have been several examples of vibrational energy harvesters published in the literature over the years. However, for many applications the generated power is not yet sufficient. In this paper, a physical model for predicting the generated electric power from piezoelectric harvesting devices is introduced. The model is based on estimating the total charge generated on a piezoelectric material when it is subjected to mechanical strain as a result of bending at the fundamental resonance frequency. Based on Euler-Bernoulli beam theory, the strain can be determined in terms of the beam deflection at purely mechanical excitation. The proposed model extends the current state of the art by consideration of the strain distribution due to the presence of an extended mass volume at the end of the beam. The constitutive equations of piezoelectricity in the sensing mode correlate the strain and the induced charge in the piezoelectric element. Using the device design parameters and the beam deflection as inputs, the power output can be calculated. The results of the model were experimentally verified for MEMS-based PHDs. The model was found to give an accurate prediction of the electrical parameters under various damping conditions. After model validation, a subsequent device optimization has been made to improve the power generation.
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