Electromechanical modeling and analysis of a piezocomposite multi-point loaded beam vibration energy harvester

In this paper, vibration energy harvesting from a piezocomposite beam with unconventional boundary conditions is investigated. The beam in consideration has multi-point constraints and consequently has concentrated multi-point loading along its length. It is shown that the natural frequencies, strain uniformity along the beam, and strain node positions can be adjusted by shifting the support locations, allowing for a significant range of mechanical tuning. To model the electromechanical system, the Euler-Bernoulli beam assumptions are adopted, and by Hamilton's principle and Gauss' law, the governing equations are derived. Frequency response functions of the output voltage and beam transverse displacement are solved for harmonic base excitation, and the maximum output power is calculated both numerically and analytically. A set of experimental results are used to validate the model. A detailed parametric analysis is conducted by varying tunable system parameters such as resistive load, tip mass, and the intermediate support location. All interesting operational conditions of the system, and the corresponding tuning parameters are quantified. It is shown that the multi-point loaded beam concept can produce higher strain-normalized-output-power when compared to a cantilevered or a simply supported beam.