Dynamic analysis of a functionally graded piezoelectric energy harvester under magnetic interaction

Abstract

The aim of this embodiment is to present an analytical analysis of a functionally graded piezoelectric energy harvester consisting of a flexible functionally graded piezoelectric layers carrying magnetic mass at the free end. The magnetic tip mass is in interaction with a permanent magnet which is located at a distance from the top of the tip mass. The oscillation of the harvester happens via excitation of the base. Using Rayleigh’s beam theory and Hamilton’s principle and considering geometric nonlinearity, the coupled electromechanical governing equations have been developed. The nonlinear frequency response of the piezoelectric energy harvester beam has also been studied under base excitation. A parametric study has been carried out to investigate the effect of grading index and magnetic force on responses of both free vibration and induced excitation cases. The results were compared with those obtained using three-dimensional finite element model developed in COMSOL Multiphysics 5.5 commercial software and good agreement has been observed. The results from both the analytical method and simulation confirm that tuning the design parameters of grading index and magnetic gap to the optimal value results in a considerable change in the performance of the energy harvester.

Harvesting energy from shock environments via functionally graded magneto-electro-elastic materials

“…According to equations ( 46)-( 48) and ( 51), it is seen that unlike the previous analytical solutions provided for piezoelectric-based systems, 14,16 the present procedure can successfully capture the dependence of the vibration frequency on the amplitude of motion.…”

“…56 In addition, in view of the fact that energy harvesters usually operate in environments with low-frequency excitations, one can take only the first mode shape of a cantilever as the dominant one and neglect the influence of the others. 14,16 Doing so, one gets…”

“…They also investigated the effect of the through thickness material gradient index on the frequency response of the system. Derayatifar et al 16 also provided a more efficient design for the FGPM harvester analyzed in Derayatifar et al 14 by equipping it with a magnetic tip mass interacting with a permanent magnet located at a distance from its top. They obtained the governing equations of motion similar to the way presented in Derayatifar et al 14 Besides investigating the effect of the gradient index, they also investigated the effect of the initial distance between the two magnets on the time domain and frequency responses of the system.…”

Validation and optimization of two models for the magnetic restoring forces using a multi-stable piezoelectric energy harvester

“…It has been much desirable to use vibration energy harvesters to solve costly battery replacement problem and make wireless sensor networks autonomous (Tian et al, 2018). Ambient vibration can be converted to electricity by four methods: piezoelectric (Derayatifar et al, 2021; Lu et al, 2018), electromagnetic (Halim et al, 2015; Pan et al, 2019; Williams and Yates, 1996; Zaghari et al, 2019), electrostatic (Choi et al, 2011; Koga et al, 2017; Zhang et al, 2018), and triboelectric (Tao et al, 2020; Wang et al, 2018b). The main advantages of the piezoelectric vibration energy harvesters (PVEHs) are their large power densities and ease of operation.…”