Theoretical analysis of coupled thermo-electric-elastic rotational piezoelectric energy harvesters based on Green's function and harmonic balance method

Energy harvesting technology is inevitably applied in complex excitation environments, such as railway infrastructure and aerospace. Therefore, it is necessary to explore the coupled multi-field effect on the energy harvester. This paper investigates coupled thermo-electric-elastic rotational piezoelectric energy harvesters, and the coupled multi-field equations are constructed and solved by Green's function and the harmonic balance method. The coupled temperature distribution caused by the displacement coupling effect is obtained by solving the coupled thermoelastic heat conduction equation. The finite element method and the Runge–Kutta numerical method are utilized to validate the obtained closed-form solutions of temperature distribution, displacement, and voltage, respectively. The numerical results indicate that the centrifugal stiffness coefficient has a positive correlation to the square of the rotational speed, which is beneficial to expand the operation bandwidth to 1000-2500 rpm and obtain a maximum of 130 mW. The maximum coupled temperature distribution induced by the displacement coupling effect occurs at the stress maximum near the cantilever beam fixed end and decreases along with the length direction. The electric coupling effect on the coupling temperature distribution is investigated by changing the external load resistance, the results also indicate that the coupled temperature distribution from the fixed end to the free end decreases significantly with increasing load resistance.