Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method

Abstract

This study examined the dynamic characteristics of nonlinear electrostatic pull-in behavior for shaped actuators in micro-electro-mechanical systems (MEMS). The natural frequencies of a fixed-fixed shaped beam vibrating around its statically deflected position were calculated using the differential quadrature method (DQM). The proposed model included the nonlinear interaction between the curved electrostatic field force and the shaped micro-beam, as well as the mid-plane stretching, axial residual stress and electrical field fringing effect. Very good agreement existed between the results simulated using the proposed model and the measured data. This work also investigated the micro-beam and electrode shape effect on the natural frequencies of the actuator system. Analytical results indicate that the variation in the micro-beam and the electrode shapes might not only influence the electrostatic field distribution but also significantly alter the dynamic characteristics of the micro-actuator. Analytical results demonstrate that the shaped micro-beam with curved electrode can increase the working voltage range approximately six times compared to the rectangular micro-beam and flat electrode.

Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator

“…Based on a single degree-offreedom model of the beams (n = 1), (4) can be solved with appropriate accuracy [46]. Hence, the solution is constructed by expressing the deflection function W (ξ , τ) as the product of two separate functions:…”

“…Examples of MEMS device applications include inkjet-printer cartridges, accelerometers, miniature robots, microengines, locks, inertial sensors, microtransmissions, micromirrors, micro actuators, optical scanners, fluid pumps, transducers, and chemical, pressure and flow sensors. New applications are emerging as the existing technology is applied to the miniaturization and integration of conventional devices [4]. However, electrostatic actuation, large deflections and damping caused by different sources give rise to nonlinear behaviour.…”

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

“…Di erent techniques have been proposed for nding solutions to nonlinear equations of MEMS: the di erential quadrature method [25], the nite-element method [9,10], and homotopy methods [26]. Although it is di cult to get an analytic approximation for di erent phenomena in MEMS, there are some analytic methods for nonlinear problems of microelectromechanical systems such as perturbation techniques [27,28].…”

Application of Higher Order Hamiltonian Approach to the Nonlinear Vibration of Micro Electro Mechanical Systems

“…Shooting method(Abdel-Rahman, Younis et al 2002), δ-perturbation method (He 2003), differential quadrature method (Kuang and Chen 2004) , Lindstedt-Poincaré method , integral equation method (Pouya 1997), homotopy analysis method (HAM)(Belén-dez, Beléndez et al 2008), variational approach (VA) (He 2007), Max-Min approach (He 2008, Zeng 2009, Zeng and Lee 2009 and Energy Balance Method )are some of the numerical and approximate analytical approaches could be addressed. Ganji, Azimi et al ) applied the Energy Balance Method (EBM) and Amplitude Frequency Formulation (AFF) to govern the approximate analytical solution for motion of two mechanical oscillators.…”