Coupling and tuning of modal frequencies in direct current biased microelectromechanical systems arrays

Abstract

Understanding the coupling of different modal frequencies and their tuning mechanisms has become essential to design multi-frequency MEMS devices. In this work, we fabricate a MEMS beam with fixed boundaries separated from two side electrodes and a bottom electrode. Subsequently, we perform experiments to obtain the frequency variation of in-plane and out-ofplane mechanical modes of the microbeam with respect to both DC bias and laser heating. We show that the frequencies of the two modes coincide at a certain DC bias, which in turn can also be varied due to temperature. Subsequently, we develop a theoretical model to predict the variation of the two modes and their coupling due to a variable gap between the microbeam and electrodes, initial tension, and fringing field coefficients. Finally, we discuss the influence of frequency tuning parameters in arrays of 3, 33, and 40 microbeams, respectively. It is also found that the frequency bandwidth of a microbeam array can be increased to as high as 25 kHz for a 40 microbeam array with a DC bias of 80 V. V

Nonlinear dynamics of micromechanical resonator arrays for mass sensing

“…The coefficients of Eqs. (24)(25)(26)(27) fore, they share the same bifurcation points and stability. Thus, the whole set of limits points on the two response curves without coupling terms are present on each response with coupling terms.…”

“…For example Gutschmidt et al studied a beam array in a 1:1 resonance configuration as well as 3:1 internal resonances near 75 pull-in [23,24,25,26]. Kambali et al [27] focused on understanding the couplings of several modal frequencies and their tuning mechanisms. In the study, modal frequencies were tuned by adjusting the continuous actuation voltage in order to rescale the beam array into a specific configuration.…”

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped–Clamped Microbeams for Mass Sensing

“…The mode coupled vibration can introduce rich nonlinear phenomena into the MEMS research and reveal the mechanism of the complex dynamic behaviors [14][15][16][17][18]. Anti-symmetric response can be induced by the mode coupled vibration.…”

“…where T n = ε n t. Substituting Equations (16) and (A8) into Equation 15and equating coefficients of like powers of ε yield O ε 1 :…”

Nonlinear dynamics for estimating the tip radius in atomic force microscopy

“…In AFM experiments, a lock-in amplifier is used to measure the amplitude and phase of the cantilever deflection signal with no contribution from higher modes and the absence of any internal resonance. 16 It is therefore valid to model the cantilever as a single-degree-of-freedom model as follows:…”