Utilizing Energy Localization in Weakly Coupled Nonlinear Resonators for Sensing Applications

Pandit, Milind; Zhao, Chun; Sobreviela, Guillermo; Du, Sijun; Zou, Xudong; Seshia, Ashwin A.

doi:10.1109/jmems.2019.2894953

Cited by 31 publications

(18 citation statements)

References 32 publications

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“…Consider the closed-loop mode-localized oscillator in Fig. 2, whose architecture is similar to the one in [14] In the absence of mismatch ( , = , , = , , = , = , = 0, = 0), we find from (7) and (31), that two oscillation states are possible, with 0 = 0 = (hence 0 = 1) and…”

Section: Iii-b Mode-localized Oscillatormentioning

confidence: 99%

“…Transient simulations of (1) clearly confirm these results. To the best of our knowledge, the experimental studies of nonlinear MOLOs available in the literature (see [30], or [31] published after the initial submission of this paper) are limited to the analysis of a single oscillation state, or of both oscillation states below the critical amplitude (37), and do not contradict them.…”

Section: Iii-b Mode-localized Oscillatormentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

Jerome

Mostafa

Ferreira

2019

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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This theoretical work investigates the properties of nonlinearlyoperated weakly-coupled resonators (WCRs) for resonant sensing applications. We propose an analysis framework for mutually injection-locked oscillators (MILOs) and mode-localized oscillators (MOLOs), subject to nonlinear restoring and damping forces. Under some simplifying assumptions, three sensor architectures are investigated and compared, highlighting several common features such as: (i) the insensitivity of the amplitude ratio output metric to the Af effect, (ii) the instability of one oscillation state above a threshold amplitude. These results are illustrated and validated using transient simulations. Their range of validity is then discussed with respect to finite perturbations, finite bandwidth, measurement noise and nonlinear dissipation-fluctuation. While nonlinear operation of WCRs has been experimentally investigated in [9, 14-15], and nonlinear coupling of FM resonant sensors or oscillators was covered in [16], there is little theoretical background against which experimental results obtained with nonlinear WCRs can be tested. Our own work on this subject [9, 17] has highlighted that some MILOs may benefit from nonlinear operation. In particular, the increase of the measurement range of MILOs, with a trade-off in sensitivity, was theoretically and experimentally proven in [9]. Most interestingly, the analysis in [17] showed the resolution of a MILO based on two similar Duffing resonators may not be limited by the A-f effect [18] provided amplitude-ratio was used as an output metric instead of phasedifference. To this day, no similar study has been performed on MOLOs. Furthermore, the results in [17] are limited to a narrow framework: a specific MILO architecture, only nonlinear restoring forces and quasi-static perturbations being considered. With this paper, we establish the fundamental limitations of WCRs in the nonlinear regime, aiming at a general, qualitative description of their behavior, rather than at particular results. The analysis of WCRs presented in section II may be used for MILOs or MOLOs; it is slightly simplified compared to the one in [17], but is more general in the sense that it captures dynamic system fluctuations (i.e. finite sensor bandwidth). Furthermore, it is not only valid for resonators with nonlinear restoring forces (e.g stress-stiffening, or electrostatic softening [19]), but also with nonlinear damping forces. Nonlinear damping is ubiquitous in MEMS sensors: for instance, it may result from the squeezed-film phenomenon [20], from anchor loss [21], or from coupling to an undesired vibration mode [22]. A global outlook on the nonlinear properties of WCRs with quadratic stiffness and damping coefficients is derived in sections III and IV. In section III, three WCR architectures are investigated, and their properties are established with further simplifying assumptions. We find that the insensitivity of AM WCRs to the A-f effect holds in all the studied cases. In section IV, these results are illustrated and ...

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Section: Iii-b Mode-localized Oscillatormentioning

confidence: 99%

Section: Iii-b Mode-localized Oscillatormentioning

confidence: 99%

Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

Jerome

Mostafa

Ferreira

2019

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…Li et al [ 21 ] presented coupled vibration behavior between second-order and third-order modes caused by the axial stress, which can be used to realize high precision parameter identification by an antisymmetric mode. In addition, weakly coupled nonlinear MEMS resonators can lead to mode localization, which can greatly improve the sensitivity of the sensor [ 22 ]. Antonio et al [ 23 ] used coupled-mode vibration to propose a novel method in order to realize frequency stabilization by coupling two different vibration modes.…”

Section: Introductionmentioning

confidence: 99%

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Liu

Shao

et al. 2021

Micromachines

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Frequency stabilization can overcome the dependence of resonance frequency on amplitude in nonlinear microelectromechanical systems, which is potentially useful in nonlinear mass sensor. In this paper, the physical conditions for frequency stabilization are presented theoretically, and the influence of system parameters on frequency stabilization is analyzed. Firstly, a nonlinear mechanically coupled resonant structure is designed with a nonlinear force composed of a pair of bias voltages and an alternating current (AC) harmonic load. We study coupled-mode vibration and derive the expression of resonance frequency in the nonlinear regime by utilizing perturbation and bifurcation analysis. It is found that improving the quality factor of the system is crucial to realize the frequency stabilization. Typically, stochastic dynamic equation is introduced to prove that the coupled resonant structure can overcome the influence of voltage fluctuation on resonance frequency and improve the robustness of the sensor. In addition, a novel parameter identification method is proposed by using frequency stabilization and bifurcation jumping, which effectively avoids resonance frequency shifts caused by driving voltage. Finally, numerical studies are introduced to verify the mass detection method. The results in this paper can be used to guide the design of a nonlinear sensor.

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“…In the past few years, in the MEMS community, a paradigm shift is observed in the design and implementation of micromechanical resonating sensors. A new perspective is presented in using 1-d chain of a coupled resonating proof masses, more familiarly refereed as multi degree-of-freedom (m-DoF) array, coupled resonator (CR) array, weakly coupled resonators (WCR) or mode-localized sensors [20][21][22][23][24][25][26][27][28]. Figure 1 shows a representative schematic for such system.…”

Section: Introductionmentioning

confidence: 99%

Ultra-Precise MEMS Based Bio-Sensors

Pachkawade¹

2021

Biosensors - Current and Novel Strategies for Biosensing

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This chapter evaluated the state-of-the art MEMS sensors used for bio sensing applications. A new class of resonant micro sensor is studied. A sensor structure based on the array of weakly coupled resonators is presented. It is shown that due to the weak coupling employed between the resonators in an array manifest ultra-high sensitivity of the output to the added analytes/biomolecules. Due to the highlyprecise output of such bio-sensors, minimum detectable mass in the range of subactogram is also possible using such MEMS sensors. Analytical modeling of such micro biosensors is presented in this chapter to understand the key performance parameters. Furthermore, role of these new classes of MEMS resonant biosensors operating at ambient temperature and/or pressure is also discussed.

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Utilizing Energy Localization in Weakly Coupled Nonlinear Resonators for Sensing Applications

Cited by 31 publications

References 32 publications

Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Ultra-Precise MEMS Based Bio-Sensors

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