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

Abstract

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.

A multi-sensing scheme based on nonlinear coupled micromachined resonators

“…This section discusses the nonlinear behaviour of the weakly coupled system. Continuous analyses using the shooting technique [38] are conducted to verify the effect of the different physical parameters. The referred parameters are given in Table 1.…”

“…1, the multi-sensing scheme comprises a weakly coupled resonator, including cantilever and bridge resonators, mechanically coupled by a thin beam. The coupling strength could be controlled by changing the coupling position, the moment of inertia, and the coupling beam's length [38]. The detailed geometric parameters and physical properties of the coupled resonator system, considered to be fabricated from silicon, are listed in Table 1.…”

Coupled Double Closed-Loop Control for an MEMS Resonant Accelerometer

“…They are also characterized by their output frequency and have outstanding anti-interference performance. They are widely used in measuring mass, acceleration, pressure, and so on [ 1 , 2 , 3 ]. Micromechanical resonant sensors must satisfy the whole system phase and amplitude balance condition [ 4 , 5 ].…”

“…In system dynamics analysis, the microresonator is equivalent to a second-order linear system [ 8 ]. However, it is reported that the microresonator is no longer equivalent to a second-order system under large amplitude vibration and behaves as a nonlinear higher-order oscillator [ 2 , 9 , 10 ]. The numerical modeling of the microresonator is not scientific enough and does not combine with the actual manufacturing size [ 11 , 12 ].…”

Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators

“…Micro-and nanomechanical resonators have been shown to be ultra sensitive for charge, force and mass measurements in the nonlinear regime [1][2][3][4][5][6]. However, the high sensitivity also renders the resonators susceptible to environmental fluctuations such as thermal noise [7][8][9] or molecular motion [10,11], thereby limiting their applications.…”