Dynamics of the round sensing element of a nanoelectromechanical sensor

Abstract

The theory of nonlinear dynamics of the circular sensing element of a nanoelectromechanical sensor in the form of flexible elastic axisymmetric nano plates is constructed. The developed theory is general. It is based on the kinematic model of the third approximation (Sheremetev-Pelekh-Reddy). Two other theories follow from it as a special case: the theory of nonlinear dynamics and flexible nano-plates, obtained on the basis of the kinematic model of the first approximation (Kirchhoff), the second approximation (Timoshenko). The general theory obtained follows from the variational principle of Hamilton. For each of the kinematic hypotheses, a system of nonlinear partial differential equations is obtained. Obtaining a “true” solution is guaranteed using the methodology outlined in [1]. As an example, the model of the first approximation of the nonlinear dynamics of flexible elastic axisymmetric nano-plates is studied. In a numerical experiment, the required equations are solved by different methods, their convergence is investigated. It is shown that taking into account the size-dependent parameter significantly affects the character of plate oscillation and changes their character.