An analytical model of a broadband magnetic energy nanoharvester array with consideration of flexoelectricity and surface effect

Based on Hamilton's principle and Mindlin plate theory, a series of 2D equations to describe the mechanical behaviors of magneto-electro-elastic (MEE) laminated nanoplates, is established for the first time with consideration of flexoelectricity and surface effect. The equations derived are general, which not only can be reduced to the corresponding piezoelectric, piezomagnetic, and elastic cases, but can also be degenerated to the classical higher-order plate theory of conventional macroscopic MEE laminates if flexoelectricity and surface effect are neglected. As the typical application, a flexoelectric magnetic energy nanoharvester array with surface effect, consisting of a giant magnetostrictive material Terfenol-D with a nonlinear magneto-thermo-mechanical coupling constitutive relation and a linear piezoelectric layer PZT-4, is investigated systematically under coupled extensional and flexural deformations. After the correctness is confirmed, an important performance index (i.e. output current) of the harvester is discussed for different conditions, including flexoelectricity, surface effect, and nonlinear magneto-mechanical coupling. It has been revealed that flexoelectricity, surface effect, external magnetic field, and pre-stress can dramatically improve the performance of characteristics such as resonant frequencies, bandwidth, and output current of the nanoharvester. Especially, a critical thickness corresponding to the flexoelectricity or surface effect is proposed, below which the size-dependent effect is obvious and must be considered. The current work can be viewed as an innovative theoretical tool for evaluating the size-dependent and nonlinear characteristics qualitatively and quantitatively, which is essential and crucial to understanding the physical and mechanical properties of MEE nanostructures.