Parameter identification and optimization in piezoelectric energy harvesting: analytical relations, asymptotic analyses, and experimental validations

Mathematical analyses of distributed-parameter piezoelectric energy harvester equations are presented for parameter identification and optimization. The focus is placed on the single-mode voltage and vibration frequency response functions (FRFs) per translational base acceleration. Asymptotic trends of the voltage output and the tip displacement FRFs are investigated and expressions are obtained for the extreme conditions of the load resistance. The relationship between the linear voltage asymptotes and the optimal load resistance is discussed. Resonance frequencies of the voltage and the tip displacement FRFs are obtained accounting for the presence of mechanical losses. Closed-form expressions are extracted for the optimal electrical loads of maximum power generation at the short-circuit and open-circuit resonance frequencies of the voltage FRF. Analytical relations are given also for the identification of modal mechanical damping both from the voltage and the vibration FRFs using a single data point. Vibration attenuation and amplification due to resonance frequency shift is also addressed. An experimental case study is presented to validate some of the major equations derived here.