Investigation of electrically actuated geometrically nonlinear clamped circular nanoplate

• Published in: Acta mechanica 2024-02, Vol.235 (2), p.1015-1026
• Main Authors: Andrianov, I. V., Koblik, S. G., Starushenko, G. A.
• Format: Article
• Language: English
• Subjects: Algorithms; Clamping; Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Geometric nonlinearity; Heat and Mass Transfer; Original Paper; Solid Mechanics; Theoretical and Applied Mechanics; Van der Waals forces; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-023-03783-0

In this paper, oscillations of the electrically actuated nonlinear clamped circular nanoplate are considered. The pull-in phenomenon, i.e., the transition of the oscillatory regime to the attraction one, is studied. Original PDE takes into account Coulomb, Casimir and van der Waals forces and geometrical nonlinearity of plate. A simple and physically clear algorithm for determining the DC voltage values at which the system suddenly collapses is proposed. This algorithm is based on the criterion consisting in the merging of points of a stable equilibrium (center) and an unstable equilibrium (saddle). Comparisons with the results obtained by other authors show sufficient accuracy of the proposed algorithm. The influence of geometric nonlinearity on pull-in values is studied. It is shown that neglect of this factor can lead to significant errors. Influence of Casimir and van der Waals forces on the pull-in value is estimated. It is shown that the dependence of the pull-in value on the initial displacements in the radial direction is almost linear.