Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

Abstract

Abstract. In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam a ected by an electric eld, including the fringing eld e ect, was obtained based on strain gradient elasticity, couple stress, and classical theory. In uences of di erent parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear di erential equation was also solved by using the Homotopy Analysis Method (HAM). The in uence of HAM parameters on accuracy was studied speci cally in the vicinity of the pull-in voltage. Comparison of the results of pull-in voltage indicated that low-voltage good agreement exists between numerical and semi-analytical methods, while HAM results deviated from those of numerical methods at high voltages. Findings indicate that strain gradient and couple stress e ects result in a sti er microbeam than with classical theory. E ects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at di erent voltages and orders of HAM approximation.

A Parametric Study of Mechanical Cross-Coupling in Parallel-Kinematics Piezo-Flexural Nano-Positioning Systems

“…The second and third authors have the same contribution. advanced technologies such as precision metrology, scanning probe microscopy [1]- [7], energy harvesting [8] [9] [10] [11], medical robotics [12] [13], biomechanics research apparatus [14]- [20], orthodontics [21] [22] [23], material [24] [25] [26], structural engineering [27] [28], microfluidic devices [29] [30] [31] [32] [33] and other instruments which need precise actuation. Several different factors limit the precision positioning of PPNP stages, including mechanical vibrations, external disturbances, hysteresis and creep effects, temperature variation, and the cross-coupling of the different axes.…”