Dynamic characteristic analysis of an electrostatically-actuated circular nanoplate subject to surface effects

• Published in: Applied Mathematical Modelling Vol. 63; pp. 18 - 31
• Main Authors: Lin, Ming-Xian, Lee, Sen-Yung, Chen, Cha'o-Kuang
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.11.2018; Elsevier BV
• Subjects: Actuation; Actuator; Circular nanoplate; Circularity; Differential equations; Differential transformation method; Dynamic response; Electric potential; Electrostatics; Fluid mechanics; Mathematical models; Modulus of elasticity; Nonlinear analysis; Numerical methods; Production methods; Pull-in voltage; Surface effect; Surface effect; Circular nanoplate; Differential transformation method; Pull-in voltage; Actuator
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.06.004

•The accuracy of hybrid scheme were found to be in good agreement with different numerical methods.•Hybrid a differential transformation and finite differences is applied to solve the problems.•The relationship between the thickness, radius, and gap of a circular nanoplate, and its voltage, is scale-dependent•The influence of surface stress and surface elastic modulus on the pull-in voltage of circular nanoplate is studied.•Surface effects is seen to have a significant role in determining the nonlinear dynamic behavior of circular NEMs. This study investigates the influence of surface effect on the nonlinear behavior of an electrostatically actuated circular nanoplate. The Casimir force, surface effects, and the electrostatic force are modelled. In performing the analysis, the nonlinear governing equation of a circular nanoplate is solved using a hybrid computational scheme combining a differential transformation and finite differences. The method is used to model systems found in previous literature using different methods, producing consistent results, thus verifying that it is suitable for treatment of the nonlinear electrostatic coupling phenomenon. The obtained results from numerical methods demonstrated that the relationship between the thickness, radius, and gap size of a circular nanoplate, and its pull-in voltage, is scale-dependent. The model exhibits size-dependent behavior, showing that surface effects significantly influence the dynamic response of circular nanoplate actuators. Moreover, the influence of surface stress on the pull-in voltage of circular nanoplate is found to be more significant than the influence of surface elastic modulus. Finally, the effects of actuation voltage, excitation frequency, and surface effects on the dynamic behavior of the nanoplate are examined through use of phase portraits. Overall, the results show that the using hybrid method here presented is a suitable technique for analyzing nonlinear behavior characteristic of circular nanoplates.