Modeling of a nanoscale flexoelectric energy harvester with surface effects

This work presents the modeling of a beam energy harvester scavenging energy from ambient vibration based on the phenomenon of flexoelectricity. By considering surface elasticity, residual surface stress, surface piezoelectricity and bulk flexoelectricity, a modified Euler-Bernoulli beam model for the energy harvester is developed. After deriving the requisite energy expressions, the extended Hamilton's principle and the assumed modes method are employed to obtain the discrete electromechanical Euler-Lagrange's equations. Then, the expressions of the steady-state electromechanical responses are given for harmonic base excitation. Numerical simulations are conducted to show the output voltage and the output power of the flexoelectric energy harvesters with different materials and sizes. Particular emphasis is given to the surface effects on the performance of the energy harvesters. It is found that the surface effects are sensitive to the beam geometries and the surface material constants, and the effect of residual surface stress is more significant than that of the surface elasticity and the surface piezoelectricity. The axial deformation of the beam is also considered in the model to account for the electromechanical coupling due to piezoelectricity, and results indicate that piezoelectricity will diminish the output electrical quantities for the case investigated. This work could lead to the development of flexoelectric energy harvesters that can make the micro- and nanoscale sensor systems autonomous.