Non-Local Piezoelasticity To Incorporate the Influence of Small-Scale Factors on the Resonance Behavior of the Mindlin Piezoelectric Polymeric Nanoplates

Abstract

This study presents an investigation into the vibration resonance of Mindlin piezoelectric polymeric nanoplates under electromechanical loading, particularly in the presence of a rotating nanoparticle. The novelty of this research lies in the application of non-local piezoelasticity, which effectively incorporates the influence of small-scale factors on the resonance behavior of the nanoplate. By employing a variational approach to derive the governing equations, this work advances the understanding of how various parameters such as the non-local parameter, dimensions of the nanoplate, excitation voltage, and mass of the nanoparticle affect resonance frequencies. The Galerkin method is utilized to solve the partial differential equations governing the dynamics of the piezoelectric polymeric nanoplate, marking a significant methodological contribution to the field. The incremental harmonic balance approach is then applied to estimate the system's resonance frequencies, with numerical simulations confirming their existence. This research not only elucidates the complex interactions affecting resonance behavior but also highlights the potential for optimizing the design of nanostructures in various applications, including sensors and energy-harvesting devices. The findings suggest that increasing the non-local parameter softens the nanoplate's rigidity, leading to decreased resonance frequencies, while modifications in dimensions and applied voltages can enhance these frequencies. Overall, this study lays the groundwork for future explorations into the dynamic behavior of piezoelectric materials, emphasizing the importance of small-scale effects in nanotechnology applications. © 2025 The Authors