Dynamic characteristics analysis of a multi-layer cantilever beam-type rotational piezoelectric energy harvester based on the Timoshenko beam model

This paper presents a rotational piezoelectric energy harvester (RPVEH) based on the Timoshenko beam model. The system comprises a five-layer composite cantilever beam with a tip magnet and two external magnets, creating a tri-stable potential energy function curve during vibration. The dynamic response expression of the system is derived using the generalized Hamilton’s principle, and the output power of the RPVEH is analyzed based on the harmonic balance method. The differences between the Timoshenko beam and the Euler beam models for various composite cantilever beam thicknesses are examined. Both sweep frequency and analytical results indicate that, under the same total beam thickness, the five-layer composite cantilever beam (0 < rs ≤ 0.8) captures more rotational energy over a wider speed range than the traditional three-layer composite cantilever beam (rs = 0). At a constant beam thickness (hb = 0.45 mm), as the beam length l increases, the peak power output of the five-layer composite cantilever beam is significantly improved compared to the traditional three-layer composite cantilever beam configuration: by 76%, 52%, and 19%, respectively (0.248 vs 0.141 W; 0.276 vs 0.181 W; 0.281 vs 0.237 W), accompanied by a 76% increase in power density for the 65 mm beam length. In addition, energy harvesting efficiency of the system under different substrate layer materials and thickness configurations is analyzed. It is found that using a cobalt alloy as the metal layer, which has a similar density and elastic modulus to the piezoelectric layer, significantly enhances the energy harvesting efficiency of the system.