A Novel Dual-Mass Accelerometer Exploiting Mode Localization in Electrostatically Coupled Resonators

2021 ◽  
Author(s):  
Ming Lyu ◽  
Jian Zhao ◽  
Najib Kacem ◽  
Pengbo Liu
Keyword(s):  
Coupling Strength ◽  
Axial Load ◽  
Amplitude Ratio ◽  
Coupled System ◽  
Inertial Forces ◽  
Governing Equations ◽  
Coupled Resonators ◽  
Critical Amplitude ◽  
Mode Localization ◽  
Vibration Magnitude

Abstract A novel dual-mass accelerometer is proposed while exploiting the phenomenon of mode localization in two electrostatically coupled resonators with an adjustable coupling strength. The external inertial forces are transmitted differentially to the resonators in term of axial load change through the two levering mechanisms, breaking the balanced state and resulting in a drastic change in the amplitudes of the two resonators. Based on the Euler Bernoulli theory, the governing equations of the coupled system are derived and numerically solved. The sensitivity in term of relative shift of amplitude ratio can be improved by 4 orders of magnitude compared to frequency shift. Finally, the effect of the quality factor on the sensor dynamics has also been investigated, and the results show that it only affects the vibration magnitude of the resonators while operating below the critical amplitude.

scholarly journals An asymmetric mode-localized mass sensor based on the electrostatic coupling of different structural modes with distributed electrodes

2021 ◽  
Author(s):  
Jiahao Song ◽  
Ming Lyu ◽  
Najib Kacem ◽  
Jian Zhao ◽  
Pengbo Liu ◽  
...  
Keyword(s):  
Amplitude Ratio ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Mass Sensor ◽  
Mass Detection ◽  
Coupled Resonators ◽  
Critical Amplitude ◽  
Asymmetric Mode ◽  
Mode Localization ◽  
Electrostatic Coupling

Abstract Mode-localization sensor with amplitude ratio as output metric has shown excellent potential in the field of micro-mass detection. In this paper, an asymmetric mode -localized mass sensor with a pair of electrostatically coupled resonators of different thickness is proposed. Partially distributed electrodes are introduced to ensure the asymmetric mode coupling of second and third order modes while actuating the thinner resonator by the distributed electrode. The analytical dynamic model is established by Euler–Bernoulli theory and solved by harmonic balance method (HBM) combined with asymptotic numerical method (ANM). Detailed investigations on the linear and nonlinear behavior, critical amplitude as well as the sensitivity of the sensor are performed. The sensitivity of the proposed sensor can be enhanced by about 20 times compared to first order mode-localized mass sensors. Furthermore, by exploiting the nonlinearities while driving the device beyond the critical amplitude for the in-phase mode, the sensor performs a great improvement in sensitivity up to 1.78 times. Besides, the influence of the decrease of coupling voltage is studied, which gives a good reference to avoid mode aliasing.

scholarly journals A Low-g MEMS Accelerometer with High Sensitivity, Low Nonlinearity and Large Dynamic Range Based on Mode-Localization of 3-DoF Weakly Coupled Resonators

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 310
Author(s):  
Muhammad Mubasher Saleem ◽  
Shayaan Saghir ◽  
Syed Ali Raza Bukhari ◽  
Amir Hamza ◽  
Rana Iqtidar Shakoor ◽  
...  
Keyword(s):  
Microelectromechanical Systems ◽  
Dynamic Range ◽  
Proof Mass ◽  
Amplitude Ratio ◽  
Silicon On Insulator ◽  
Coupled Resonators ◽  
Mode Localization ◽  
Mems Accelerometer ◽  
Weakly Coupled ◽  
Input Acceleration

This paper presents a new design of microelectromechanical systems (MEMS) based low-g accelerometer utilizing mode-localization effect in the three degree-of-freedom (3-DoF) weakly coupled MEMS resonators. Two sets of the 3-DoF mechanically coupled resonators are used on either side of the single proof mass and difference in the amplitude ratio of two resonator sets is considered as an output metric for the input acceleration measurement. The proof mass is electrostatically coupled to the perturbation resonators and for the sensitivity and input dynamic range tuning of MEMS accelerometer, electrostatic electrodes are used with each resonator in two sets of 3-DoF coupled resonators. The MEMS accelerometer is designed considering the foundry process constraints of silicon-on-insulator multi-user MEMS processes (SOIMUMPs). The performance of the MEMS accelerometer is analyzed through finite-element-method (FEM) based simulations. The sensitivity of the MEMS accelerometer in terms of amplitude ratio difference is obtained as 10.61/g for an input acceleration range of ±2 g with thermomechanical noise based resolution of 0.22 and nonlinearity less than 0.5%.

Investigating Mode Localization at Lower- and Higher-Order Modes in Mechanically Coupled MEMS Resonators

2020 ◽  
Vol 15 (3) ◽  
Author(s):  
Hassen M. Ouakad ◽  
Saad Ilyas ◽  
Mohammad I. Younis
Keyword(s):  
Coupled System ◽  
Higher Order ◽  
Coupling Beam ◽  
Coupled Resonators ◽  
Mode Localization ◽  
Practical Applications ◽  
Higher Order Modes ◽  
Mems Resonators ◽  
Selective Localization ◽  
Forced Vibration Analysis

Abstract Mode localization is investigated in a weakly mechanically coupled system. The system comprises of two doubly clamped microbeams mechanically linked with a coupling beam close to the anchors. The phenomenon is explored among the first three vibration modes pairs, each consisting of an in-phase and out-of-phase mode. A distributed-parameter model accounting for the two mechanically coupled resonators, the coupling beam, and their geometric and electric nonlinearities are derived using the extended Hamilton's principle. A reduced-order model is then derived from the Lagrangian of the equations. An eigenvalue analysis is performed under different side electrode bias scenarios. The voltage bias impact on the natural frequencies of the pairs of modes is investigated. Veering among the various modes is observed and studied as varying the bias conditions. It is demonstrated that the veering zones can be greatly affected, tuned, and shifted by the biasing voltages. Finally, forced vibration analysis is performed. It is observed that the choice of the resonator to be excited, perturbed, and its response to be monitored is very important to fully understand and utilize the localization phenomenon for practical applications. Further, it is observed that very weak coupling is required to activate mode localization in higher-order modes. The reported selective localization and activation and deactivation of higher-order modes can be potentially useful for various applications, such as parallel mechanical computing, and for ultra-sensitive in high-frequency environments.

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

scholarly journals Galvanic Phase Coupling of Superconducting Flux Qubits

2021 ◽  
Vol 11 (23) ◽  
pp. 11309
Author(s):  
Mun Dae Kim
Keyword(s):  
Coupling Strength ◽  
Fault Tolerant ◽  
Coupled System ◽  
Inductive Coupling ◽  
Galvanic Coupling ◽  
Flux Qubits ◽  
Superconducting Flux Qubits ◽  
Qubit Gate ◽  
Central Loop ◽  
Fundamental Boundary

We investigate the galvanic coupling schemes of superconducting flux qubits. From the fundamental boundary conditions, we obtain the effective potential of the coupled system of two or three flux qubits to provide the exact Lagrangian of the system. While usually the two-qubit gate has been investigated approximately, in this study we derive the exact inductive coupling strength between two flux qubits coupled directly and coupled through a connecting central loop. We observe that the inductive coupling strength needs to be included exactly to satisfy the criteria of fault-tolerant quantum computing.

scholarly journals Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

2018 ◽  
Vol 45 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Meraj Alam ◽  
Bibaswan Dey ◽  
Sekhar Raja
Keyword(s):  
Solid Tumor ◽  
Solid Phase ◽  
Fluid Motion ◽  
Extracellular Fluid ◽  
Mixture Theory ◽  
Coupled System ◽  
Weak Sense ◽  
Governing Equations ◽  
One Dimensional ◽  
2D And 3D

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska?Brezzi) condition and Lax?Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on ??2 and Sobolev norms. We discuss the so-called phenomena of ?necrosis? inside a solid tumor using the energy of the system.

Mode Localization in Two Coupled Nearly Identical MEMS Cantilevers for Mass Sensing

2019 ◽  
Author(s):  
Toky Rabenimanana ◽  
Vincent Walter ◽  
Najib Kacem ◽  
Patrice Le Moal ◽  
Gilles Bourbon ◽  
...  
Keyword(s):  
Amplitude Ratio ◽  
Actuation Voltage ◽  
Beam Theory ◽  
Mass Detection ◽  
Mass Sensing ◽  
Experimental Frequency ◽  
Mode Localization ◽  
Dc Voltage ◽  
Geometrical Imperfections ◽  
Mems Cantilevers

Abstract This paper investigates the mass sensing in a mode-localized sensor composed of two weakly coupled MEMS cantilevers with lengths 98μm and 100μm. The two resonators are connected by a coupling beam near the fixed end, and the shortest cantilever is electrostatically actuated with a combined AC-DC voltage. The DC actuation voltage is tuned to compensate the length difference and geometrical imperfections in order to dynamically equilibrate the system. An analytical model of the device using the Euler Bernoulli beam theory is presented and the required DC voltage to reach the balanced state is used. A mass perturbation is then added on the long cantilever and the eigenstate shifts and amplitude ratios in each mode are calculated for different couplings. Results show that the amplitude ratio of the second mode is the best output metric for the mass detection. For the validation of the model, an experimental investigation is carried out by using devices fabricated with the Multi-User MEMS Processes. Three different couplings are considered and the long cantilever is designed with a mass attached at its end. Instead of adding a mass on the device, we remove this part with a probe to introduce the perturbation. When the mass is removed, the experimental frequency responses of the device show localized vibrations, which are in good agreement with the theoretical results.

Parametric Dynamics of Mistuned Bladed Disk

2014 ◽  
Author(s):  
Peiyi Wang ◽  
Lin Li
Keyword(s):  
Coupling Strength ◽  
Amplification Factor ◽  
Dynamic Properties ◽  
Forced Response ◽  
Design Parameters ◽  
Classical Dynamic ◽  
Mode Localization ◽  
Bladed Disk ◽  
Saddle Surface ◽  
Wear And Tear

The mistuning of bladed disk comes from manufacturing tolerances and in-service wear and tear. Consequently the cyclic symmetry has been destroyed by mistuning, even small mistuning levels could result in drastic changes in the dynamics of bladed disks. Specifically, mistuning can cause mode localization and an increase of the maximum forced response. It has been known that frequency veering, modal localization and magnification of response are three most classical dynamic properties of bladed disk. However few researches has focused on the relationships between dynamic characters and design parameters, because the proper variation ranges of the design parameters are difficult to be determined. The aim of this paper is to investigate the relationship between designed parameters and dynamic properties of mistuned bladed disk. Based on a lumped parametric model of bladed disk and utilizing parameterized eigenvalue solution, a reasonable range of designed parameter corresponding to specific nodal diameter index was provided. The numerical results showed that the curves of the gap of frequency veering versus coupling strength or blade stiffness have bowel-style. It was also found that there exists a quasi-saddle-surface while the vibration amplification factor varies with coupling strength and mistuning strength. The quasi-saddle-surface reveals that the existence of threshold of vibration amplification factor depends on the value of coupling strength. The result means that a proper choice of combination of coupling strength and mistuning strength could lead to a suppression of mistuned vibration amplification.

Theoretical analysis of MHD Carreau liquid over a heated rotating disk under Von-Karman transformations

2019 ◽  
Vol 16 (2) ◽  
pp. 390-408 ◽  
Author(s):  
Memoona Bibi ◽  
Muhammad Sohail ◽  
Rahila Naz
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Content Type ◽  
Highly Nonlinear ◽  
Contour Plots ◽  
Optimal Homotopy Asymptotic Method

Purpose The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference. Design/methodology/approach An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly. Findings It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number. Originality/value The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.

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