Control of Spring Softening and Hardening in the Squared Daisy

Abstract

Nonlinear, mechanical microelectromechanical system (MEMS) resonating structures exhibit large displacement and a relatively broad operating bandwidth. These unique features make them particularly of interest for the development of MEMS actuators and sensors. In this work, a mechanical MEMS structure allowing the designer to determine the type of nonlinearity, that is, softening or hardening, based on its anchor scheme is presented. Effects of the excitation signal on the behavior of the proposed MEMS in the frequency domain are investigated. In this regard, a comprehensive experimental comparison among the nonlinear behaviors of softening and hardening has been conducted. To reduce the hysteresis effect to a minimum, an excitation approach, which is a pulsed sweep in frequency with a discrete resolution, is presented. The maximal velocity, quality factor, bandwidth, and resonant frequency of these two types of nonlinear MEMS resonators are compared under three different types of excitation. Finally, it is shown that the performance and characteristics extracted from nonlinear mechanical MEMS resonating structures are highly dependent on the excitation method. Hence, in the present case, the apparent performances of the MEMS resonator can increase by up to 150% or decrease by up to 21%, depending on the excitation approaches. This implies the necessity of a standardized testing methodology for nonlinear MEMS resonators for given end applications.

A Nonlinear Pulse Shaping Method Using Resonant Piezoelectric MEMS Devices

“…The behavior of H R has been simulated using MATLAB (2020B) with the ordinary differential equation solver ode45. It has then been characterized following the guidelines presented in [38]. The result of such characterization is presented in Fig.…”

“…These nonlinear resonators are based on the Squared Daisy structure presented in [39]. One interesting property of this structure is its ability leverage both types of nonlinear stiffness (either spring softening or spring hardening) depending on the anchoring scheme used, as shown in [38]. This property is especially of interest in this case as it will allow the demonstration of pulse shaping for nonlinear MEMS resonators exhibiting either either spring softening or spring hardening.…”

“…Due to the amplitude dependent nonlinear behavior of the MEMS resonator, the characterization of the devices is more complex than the characterization of a linear MEMS resonator. Work in [38] provides further details regarding the characterization methodology of the devices. This includes the generation of the excitation waveforms (PS, CSF and CSB), and their impact on the experimental characterization of the nonlinear MEMS resonators.…”

“…Changing the amplitude of the excitation signal results in a variation of F mv , such that for the STR, increasing the amplitude of the excitation signal decreases F mv as κ < 0. Frequency (Hz) Reprinted from [38].…”

“…Fig.8: Visualization of the influence of the direction of the frequency sweep on the frequency response of: (a) softening resonator (STR) (b) hardening resonator (HTR). Reprinted from[38].…”