Abstract
With the attention focused on harvesting energy from the ambient environment for nanoscale electronic devices, electromechanical coupling effects in materials have been studied for many potential applications. Flexoelectricity can be observed in all dielectric materials, coupling the strain gradients and polarization, and may lead to strong size-dependent effects at the nanoscale. This paper investigates the flexoelectric energy harvesting under the harmonic mechanical excitation, based on a model similar to the classical Euler–Bernoulli beam theory. The electric Gibbs free energy and the generalized Hamilton’s variational principle for a flexoelectric body are used to derive the coupled governing equations for flexoelectric beams. The closed-form electromechanical expressions are obtained for the steady-state response to the harmonic mechanical excitation in the flexoelectric cantilever beams. The results show that the voltage output, power density, and mechanical vibration response exhibit significant scale effects at the nanoscale. Especially, the output power density for energy harvesting has an optimal value at an intrinsic length scale. This intrinsic length is proportional to the material flexoelectric coefficient. Moreover, it is found that the optimal load resistance for peak power density depends on the beam thickness at the small scale with a critical thickness. Our research indicates that flexoelectric energy harvesting could be a valid alternative to piezoelectric energy harvesting at micro- or nanoscales.
Highlights
With the development of nanotechnology, harvesting ambient waste energy into usable energy has drawn growing attention in the last decades
Polyvinylidene difluoride (PVDF) is taken as an example material to demonstrate the effects of size and the electric resistance on flexoelectric energy harvesting
It should be noted that, the small structure considered in the present study may not be applicable for the ambient vibration energy harvesting because of its super high frequency, it is possible to design large size polyvinylidene difluoride (PVDF) energy harvesting with giant flexoelectricity [55] for the ambient vibration frequency because the optimal thickness for the maximum power density is proportional to the flexoelectric coefficient
Summary
With the development of nanotechnology, harvesting ambient waste energy into usable energy has drawn growing attention in the last decades. Based on the electric Gibbs energy, Liang et al [32] proposed the Euler–Bernoulli beam model to investigate the effect of surface and flexoelectricity on the coupling response of piezoelectric nanostructures. They found that the effective bending rigidity of the nanobeam enhances dramatically in nanoscale. Yan and Jiang [33] discussed the flexoelectric effect on the mechanical and electrical properties of piezoelectric nanobeams under static bending and different mechanical boundary conditions based on the internal energy. Liang et al [34] investigated the effect of flexoelectricity and surface on buckling and vibration behavior of piezoelectric beams by use of the Euler–Bernoulli beam model. TheREVIEW multi-mode solutions, the performance of the flexoelectric energy harvesting is analyzed in detail
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