Modeling the Size Dependent Static and Dynamic Pull-in Instability of Cantilever Nanoactuator Based on Strain Gradient Theory

Abstract

It is well-established that mechanical behavior of nanoscale systems is size dependent. In this paper, strain gradient elasticity theory is used for mathematical modeling of size dependent electromechanical instability of cantilever nanoactuator. The nanoactuator is modeled using Euler–Bernoulli beam theory and equation of motion is derived using Hamilton's principle. In order to solve the nonlinear governing equation, reduced order method (ROM) is employed. The dynamic pull-in instability of the nanoactuator is investigated through plotting the time history and phase portrait of the system. Static and dynamic pull-in voltage of nanoactuator as a function of dimensionless length scale parameters is determined. The obtained results show that when thickness of the nanoactuator is comparable with the intrinsic material length scales, size effect can substantially influence the pull-in behavior of the system.

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

“…The instability analysis of nano-structures on the basis of strain gradient theory cen be found in the literature [31][32][33][34]. In the present study, the nonlinear dynamic pull-in instability of a double-sided nano-bridge as an angular speed sensor is investigated.…”

Investigation of dynamic instability of three plates switch under step DC voltage actuation using modified couple stress theory

“…Some works have devoted to analysis of static and dynamic behavior of micro and nano structures considering the length scale parameter. Sedighi et al [27] modeled static and dynamic pull-in instability of nanoactuator based on the strain gradient theory. Pull-in instability of cantilever and fixed-fixed beam-type nano structure and nano switches using strain gradient and couple stress theory have been studied in refs.…”

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

“…In recent years, numerous studies including the static, dynamic, and thermal analyses have been accomplished on micro and nanostructures (for instances, see these studies based on the nonlocal [27,28], strain gradient [29,30], modified couple stress [31,32], and non-Fourier heat conduction theories, [33,34]). Sedighi et al [35] investigated the size dependent electromechanical instability of cantilever nano-actuator by the use of the strain gradient elasticity theory. The nanoactuator was modeled by employing the Euler-Bernoulli beam theory and the equation of motion was derived via Hamilton's principle.…”