Analytical Electromechanical Modeling of Nanoscale Flexoelectric Energy Harvesting

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.

Bending and Vibration Analysis of Flexoelectric Beam Structure on Linear Elastic Substrates

“…By the separated variables method, the characteristic equation for the natural frequency of the flexoelectric energy harvester based on a linear elastic substrate under the OCI condition can be solved. The solution of this equation can be set according to the form of Equation (38) as [31,32]:…”

Numerical Analysis of Signal Response Characteristic of Piezoelectric Energy Harvesters Embedded in Pavement

“…These are limited by the requirement of traditional centralized power supply or battery power supply. The development of low-cost, decentralized, and sustainable energy is a necessity to facilitate a wide application of embedded, off-grid sensors [4]. Environmental energy harvesting is the process of transforming the energy that exists in the environment (such as light, heat, mechanical, electromagnetic, biological, and wind energy, among others) into electricity that can be used; it is a potential way to extend the service life of embedded, off-grid sensors [5].…”

Electromechanical Analysis of Flexoelectric Nanosensors Based on Nonlocal Elasticity Theory

“…The effective elastic, dielectric, and flexoelectric properties of heterogeneous membranes were estimated in their paper. Employing these theories, the static and dynamic electromechanical responses of flexoelectric nanostructures and flexoelectric energy harvesters have been investigated [11][12][13][14][15][16][17][18]. Zhou et al [15] investigated the electromechanical responses of flexoelectric beams with three different electrical boundary conditions, in which the induced electric potential was discussed in detail.…”

“…Substituting Equation (18) into Equation (13), the mechanical equilibrium of the flexoelectric beam with the nonlocal effect can be rewritten as:…”