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Piezoelectric-based energy harvesting from bridge vibrations subjected to moving successive vehicles by functionally graded cantilever beams – Theoretical and experimental investigations

M. Mousavi, S. Ziaei-Rad and A.H. Karimi

Mechanical Systems and Signal Processing, Volume 188, December 2022, 110015



This study aims to harvest electrical energy from the vibrations of bridges. For this purpose, a functionally graded (FG) cantilever beam installed at the mid-point of a bridge was utilised. First, the motion equations for the bridge and FG harvester were acquired based on Hamilton's principle. The bridge was considered as a simply-supported Timoshenko beam, whilst the Euler-Bernoulli beam assumption was used for the FG energy harvester. The material properties were assumed to be functionally graded in the thickness direction according to the power law distribution for both the substrate and the piezoelectric layer of the harvester. The obtained equations were solved using the Runge-Kutta method. In addition, a finite element (FE) simulation was carried out in COMSOL on the bridge-FG harvester system, and a test rig was constructed to perform some empirical tests. Finally, the voltage and power obtained from the theoretical model were compared with the FE results and measured data. An excellent agreement was observed among the results. This subject indicates that the proposed model was accurate enough to predict the behaviour of the bridge and FG harvester. The maximum power harvested by the FG harvester was measured to be about 210 µW at the optimum value for the resistance.



A. Piezoelectric energy harvesting; B. Consecutive moving masses; C. Functionally graded material; D. Timoshenko beam; E. Euler-Bernoulli beam


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