Vibration energy harvesting from a piezoelectric bistable system with two symmetric stops

Abstract

Random vibration energy is widely existing in the environment. To efficiently harvest it, many researchers have designed lots of harvesters up till now. A lot of research works have found that when a harvester with bistable piezoelectric energy is excited by stochastic forces, if the intensity of them is low, the system's motion will be trapped in a single potential well. This will result in a low output voltage. In order to overcome the difficult of it and improve the harvesting efficiency, we develop an impact facility with two stops and incorporate it to a bi-stable energy harvester. This design can improve the harvesting efficiency greatly. First the electromechanical coupling equations are derived based on the Euler-Bernoulli beam theory and Kirchhoff's law. Then, we analyze the symmetric stops' effect on the potential function and the elastic restoring force of the system. Results show that both the potential energy and the magnitude of restoring force will be enhanced when collision takes place. Furthermore, we investigate the impact's effect on the system's dynamic responses and efficiency at harmonic excitation. Results reveal that a well designed impact can transform an intrawell motion into an interwell, and then increase the output voltage. And the chaotic motion can be changed into the large amplitude periodic one. Then, the harvester's dynamic responses under random excitations at a low intensity are obtained by using Euler-Maruyama method. Results indicate that the collision gaps can greatly influence the efficiency of the energy harvester. Collisions between the beam and the stops can force the system to oscillate between two potential wells more frequently. According to the relationship between the gap and the standard deviation of output voltage, we know that there exists an optimal collision gap for a definite intensity of stochastic excitation. The bistable energy harvester with this optimal gap will oscillate between the two wells frequently, and output a large voltage. Moreover, the collision stiffness can influence the system's performance as well. With the increase of collision stiffness, the system will exhibit a more frequently jumping between the two potential wells, but the stiffness has a limitation, exceeding which it cannot increase the frequency of jumping and improve the output power any more. So by properly designing the collision gap and stiffness, the system can most frequently jump between the two wells with a large amplitude of displacement, hence can attain the highest harvesting efficiency.