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With the rapid development of wearable electronics, novel power solutions are required to adapt to flexible surfaces for widespread applications, thus flexible energy harvesters have been extensively studied for their flexibility and stretchability. However, poor power output and insufficient sensitivity to environmental changes limit its widespread application in engineering practice. A doubly clamped flexible piezoelectric energy harvester (FPEH) with axial excitation is therefore proposed for higher power output in a low-frequency vibration environment. Combining the Euler-Bernoulli beam theory and the D'Alembert principle, the differential dynamic equation of the doubly clamped energy harvester is derived, in which the excitation mode of axial load with pre-deformation is considered. A numerical solution of voltage amplitude and average power is obtained using the Rayleigh-Ritz method. Output power of 22.5 μW at 27.1 Hz, with the optimal load resistance being 1 MΩ, is determined by the frequency sweeping analysis. In order to power electronic devices, the converted alternating electric energy should be rectified into direct current energy. By connecting to the MDA2500 standard rectified electric bridge, a rectified DC output voltage across the 1 MΩ load resistor is characterized to be 2.39 V. For further validation of the mechanical-electrical dynamical model of the doubly clamped flexible piezoelectric energy harvester, its output performances, including both its frequency response and resistance load matching performances, are experimentally characterized. From the experimental results, the maximum output power is 1.38 μW, with a load resistance of 5.7 MΩ at 27 Hz, and the rectified DC output voltage reaches 1.84 V, which shows coincidence with simulation results and is proved to be sufficient for powering LED electronics.

Analytical Modeling of a Doubly Clamped Flexible Piezoelectric Energy Harvester with Axial Excitation and Its Experimental Characterization