Vibration and dynamic behavior of electrostatic size-dependent micro-plates

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering 2020-08, Vol.42 (8), Article 407
• Main Authors: Karimipour, I., Tadi Beni, Y., Zeighampour, H.
• Format: Article
• Language: English
• Subjects: Aspect ratio; Compressive properties; Computer simulation; Conversion; Dynamic characteristics; Dynamic response; Electric converters; Engineering; Equations of motion; Excitation; Free vibration; Kirchhoff theory; Mechanical Engineering; Parameters; Partial differential equations; Plate theory; Residual stress; Resonant frequencies; Runge-Kutta method; Size effects; Technical Paper
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-020-02490-4

The recent trend of using thin micro-plate structures in severe operational conditions caused the classical theory (CT) to be no longer suited in analyzing the dynamic characteristics of them. For this study, the modified version of the couple stress theory (MCST) is adopted. Then, using Hamilton’s principle and Kirchhoff plate theory, the dynamic form of the size-dependent equation of motion for micro-plates stimulated by electrostatic dynamic excitation is acquired. The mixed extended Kantorovich and differential transformation methods on partial differential equations are applied to obtain the mode shapes and natural frequencies. The mode shapes from the linear free vibration solution are used as the mode shapes of the assumed multi-mode displacement field. The displacement field is required to solve the dynamical equation of motion. The equations are subsequently solved by the fourth-order Runge–Kutta method. Some universal graphs are also presented using the MCST to predict the effects of the size effect, tensile and compressive residual stresses, and aspect ratio of micro-plate on the free vibration and dynamic behaviors of micro-plates around their static configuration. It is found that the non-dimensional natural frequency parameter varies linearly versus the other non-dimensional parameters of the micro-plate. Various interesting phenomena are observed from the current simulations of the dynamic response of micro-plates to both DC and AC excitation, as well as the boundary of the frequency behavior conversion. A comparison is drawn between the responses of the micro-plate based on the modified couple stress and CT taking the size dependency into account. To facilitate understanding of the physical phenomena observed in the results, a simple physical analog to the micro-plates is suggested. This physical analog, which describes the boundary of frequency behavior conversion, is the linear relationship between the non-dimensional parameters of the system. The study of this model can help to realize some of the complex responses of the micro-plates.