Optimal design of plate-based random vibration energy harvesting system

Pasting piezoelectric thin films on a rectangular plate constitutes a practical vibration energy harvester. This manuscript investigates the optimal design of energy harvesters excited by wideband random point force with the objective to maximizing the mean output power, including the position of piezoelectric patch, the dimension and the load resistance. First, derive the stochastic partially differential-integral equations with respect to the displacement and output voltage, and then by eliminating the partial variables through modal expansion technique, the stochastic ordinary differential equation with infinite dimensions with respect to principal coordinates and voltage is derived. The analytical expression on the mean output power is derived through the linear random vibration theory, based on that the optimal design is discussed in detail. The analytical results show that as for the wideband excitation, the optimal positions of the piezoelectric patch include the self- and the symmetric positions of the exciting point. With the optimal position, the mean output power almost monotonically increases with the dimension of the piezoelectric patch and the increasing speed declines. The optimal dimension can be determined base on the above results. The optimal load resistance is derived by the existence of extreme value of the relation curve between the mean power and load resistance. This manuscript discloses the symmetry of the optimal position and the sensitivity of mean power on position of piezoelectric patch, and provides certain guidance for the design of thin plate-based vibration energy harvesters.