Nonlinearity in micromechanical free–free beam resonators: modeling and experimental verification

Abstract

In this paper, we present a systematic characterization and modeling technique for the micromechanical free-free beam resonator to analyze its nonlinear vibration behavior. Different from the conventional FEM-based approach whose simulation accuracy is usually limited around 60-70%, the proposed modeling method is able to accurately identify both the mechanical and electrostatic nonlinear parameters from just a few preliminary experimental observations. The nonlinear equation of motion is then numerically solved, demonstrating both the spring hardening and softening effects in the system. The simulated nonlinear behavior of the resonator under different driving conditions is validated by comparing them with the experimental data. In addition, based on the verified nonlinear model, design guidelines such as the nonlinearity cancellation are also highlighted. Although this work focuses on the free-free beam resonators, the proposed modeling approach can be applied to any other electrostatically driven microresonator to reveal different intrinsic nonlinear properties of the device.

Nonlinear dynamics characterization of electrostatically actuated sub-micro beam resonators

“…In the general situation with squeezz-film damping and the stiffness nonlinearities in the forced vibration of a micro-resonator, the governing equation of nonlinear vibration for the dynamic model of the electrostatically actuated micro-beam [9][10] is…”

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

“…From 2002 onward, analytical and experimental investigations of directly-excited microresonators flourished. Amongst the various analytical and experimental efforts focusing on electrostatically-actuated systems, for example, were: (i) the 2004 effort of Kaajakari et al [88], which examined the nonlinear response of silicon, bulk acoustic wave (BAW) resonators, demonstrating that these systems, in comparison to their flexural counterparts, had appreciably-higher energy storage capabilities; (ii) the 2005 work of Jeong and Ha [89], which developed a predictive model for the linear displacement limits of comb-driven resonant actuators; (iii) the 2007 and 2008 efforts of Agarwal et al [90,91], which detailed the modeling, analysis, and optimization of double-ended-tuning-fork resonators simultaneously actuated by two, variable-gap electrostatic forces; and finally, (iv) the 2008 investigation of Shao et al [92], which thoroughly detailed the nonlinear response of free-free microbeam resonators.…”

Nonlinear behavior of Lamé-mode SOI bulk resonator

“…In a previous work, flexural second mode free-free (abbreviated as "ff") beam resonator was designed and implemented using the SOIMUMPs process. The extracted model parameters of the ff beam resonator are listed in Table 2 [6]. The ff beam resonator occupies a silicon area of 650μm by 470μm, similar to the Lamé-mode resonator.…”