Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam |
| |
Authors: | Yanmei Yue Kaiyu Xu Xudong Zhang Wenjing Wang |
| |
Institution: | 1.Department of Engineering Mechanics,Shijiazhuang Tiedao University,Shijiazhuang,China;2.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University,Shanghai,China;3.Department of Mechanics, College of Science,Shanghai University,Shanghai,China;4.State Grid Cangzhou Electric Power Supply Company,Cangzhou,China;5.Department of Mechanical Engineering,University of Alberta,Edmonton, Alberta,Canada |
| |
Abstract: | A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlinear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Compared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However, the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models also have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam. |
| |
Keywords: | surface effect nonlinear strain surface residual stress fourth-order nonlinear system periodic solution existence and uniqueness asymptotic stability piezoelectric nanobeam |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《应用数学和力学(英文版)》浏览原始摘要信息 |
| 点击此处可从《应用数学和力学(英文版)》下载免费的PDF全文 |
|