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Vibro-Impcact harvesting devices are one concept to increase the bandwidth of resonant operated piezoelectric vibration generators. The fundamental setup is a piezoelectric bending element, where the deflection is limited by two stoppers. After starting the system in resonance operation the bandwidth increases towards higher frequencies as soon the deflection reach the stopper. If the stoppers are rigid, the frequency response gives constant amplitude for increasing frequencies, as long the system is treated as ideal one-DOF system with symmetric stoppers. In consequence, the bandwidth is theoretically unlimited large. However, such a system also has two major drawbacks, firstly the complicated startup mechanism and secondly the tendency to drop from the high constant branch in the frequency response on the much smaller linear branch if the system is disturbed. Nevertheless, the system has its application wherever the startup problem can be solved. Most modeling approaches utilize modal one-DOF models to describe the systems behavior and do not tread the higher harmonics of the beam. This work investigates the effects of the stoppers on the vibration shape of the piezoelectric beam, wherefore a finite element model is used. The used elements are one-dimensional two node elements based on the Timoshenko-beam theory. The finite element code is implemented in Matlab. The model is calculated utilizing time step integration for simulation, to reduce the computation time an auto-resonant calculation method is implemented. A control loop including positive feedback and saturation is used to create a self-excited system. Therefore, the system is always operated in resonance (on the backbone curve) and the frequency is a direct result of the computation. In this case tip velocity is used as feedback. This technique allows effective parametric studies. Investigated parameters include gap, excitation amplitude, tip mass as well as the stiffness of the stopper. The stress and strain distribution as well as the generated electrical power is analyzed with respect to the proper operation range.
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