Surface integrity and size dependent modeling and performance of non-uniform flexoelectric energy harvesters
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TECHNICAL PAPER
Surface integrity and size dependent modeling and performance of non-uniform flexoelectric energy harvesters E. F. Rojas1 • S. Faroughi2 • A. Abdelkefi1 • Y. H. Park1 Received: 24 March 2020 / Accepted: 30 March 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Piezoelectric energy harvesters have recently been the focus of several researchers over several years due to their effectiveness at submicron scales by including the flexoelectric effect. Though the size-dependency of the flexoelectric effect had been examined at nanoscales, the size dependent effects of the material structure had been neglected; these nanoscale models do not accurately represent models at the nanoscale. A robust reduced-order model is introduced in this study that incorporates material structure size-dependency through the couple stress theory, the effects of the surface profile by examining the average roughness and slope of roughness and the impacts of the surface stress through the Gurtin– Murdoch surface elasticity theory on a non-uniform cantilever beam energy harvester. Couple stress considerations greatly impact all examined systems, harden the system, and increase the power bandwidth whereas surface roughness influences the expected harvestable power and optimal loading of the system, by reducing expected power output. This analysis shows the importance of considering the size dependent effects on the performance of flexoelectric energy harvesters in nanoscale.
1 Introduction Piezoelectric materials have formerly been broadly applied to industrial, medical, military products, etc. Piezoelectric energy harvesters are generally designed as a bilayer or multilayered beam- or plate-like structure for energy harvesting or electric actuation (Jeong et al. 2017; Khoo et al. 2017; Chuaqui and Roque 2017; Kwon et al. 2013; Chu et al. 2019; Yang et al. 2015). There have been many studies that have outlined the behavior of piezoelectric energy harvesters at the macroscales (Raja et al. 2017; Akbar and Curiel-Sosa 2018; Hosseini and Hamedi 2016). Micro/nanoscale piezoelectric energy harvesters have gained interest from researchers, due to the applications in ferroelectric nanofilms (Jeon et al. 2005; Muralt et al.
& S. Faroughi [email protected] & A. Abdelkefi [email protected] 1
Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, USA
2
Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
2009) and non-ferroelectric nanowires (Wang and Song 2006). Recently, flexoelectricity has been increasingly studied both experimentally (Cross 2006; Catalan et al. 2004) and theoretically (Chen et al. 2015; Majdoub et al. 2008; Wang and Wang 2017; Rojas et al. 2019; Zeng et al. 2019; Wang et al. 2018). The piezoelectric effect only occurs in noncentrosymmetric crystalline materials and defines a linear relationship between mechanical strain and an electric field (Li and Luo 2017). Of all 32 cry
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