Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Abstract

This paper deals with the investigation of nonlinear static pull-in instability of smart Nano-switches regarding the new size-dependent phenomenon, known as flexoelectricity, together with the surface effects. It is noteworthy that the coupling effect of the flexoelectricity and surface elasticity on nonlinear static pull-in instability of electrostatically-actuated Nano-switches has not been studied before. Euler-Bernoulli beam assumptions in conjunction with the von-Karman nonlinearity are considered to formulate the problem. The Nano-switch is subjected to electrostatic actuation force with fringing field effect as well as Casimir force. Refined constitutive relations for piezoelectric materials capturing the flexoelectric effects are taken into consideration for mathematical modeling. Additionally, a surface elasticity approach is employed to reach an accurate model for the system. Considering the imposed electric boundary conditions, Gauss’s equation is solved to acquire the electric potential distribution along with the thickness of the Nano-switch. Thereafter, Hamilton’s principle is hired to derive the coupled nonlinear governing equations of the system. Utilizing the differential quadrature method (DQM), the nonlinear ordinary differential equations are transformed into a system of nonlinear algebraic equations. Consequently, Newton-Raphson method is exploited as a numerical method to solve the obtained algebraic equations which leads to the pull-in voltage. Investigating the maximum displacement of the Nano-switch in response to the applied electrostatic force, the effects of various involved parameters such as flexoelectricity and surface elasticity on pull-in instability are explored in detail. Furthermore, the size-dependent behavior of the pull-in instability against the flexoelectric, surface effects and applied piezoelectric voltage is analyzed. Totally, it is revealed that the flexoelectricity may exhibit a substantial influence on the pull-in behavior of smart Nano-switches, especially for some cases with small thicknesses. Therefore, this effect should be taken into account to reach an accurate, reliable and optimized design for Nano-switches.