Nonlinear Behavior of a Parametric Resonance-Based Mass Sensor

2002 ◽  
Author(s):  
Wenhua Zhang ◽  
Rajashree Baskaran ◽  
Kimberly L. Turner
Keyword(s):  
Parametric Resonance ◽  
Mathieu Equation ◽  
Nonlinear Behavior ◽  
High Sensitivity ◽  
Small Mass ◽  
Mass Change ◽  
Mass Sensor ◽  
Mass Sensors ◽  
Mems Oscillator ◽  
Harmonic Resonance

The ability to detect mass change of the order of femtograms (10e-15g) opens up implementations of various precise chemical and biological sensors. Micro-scale oscillator based mass sensors are promising due to their small mass and high sensitivity. Many such sensors detect mass change by measuring the shift of natural frequency. We have reported previous work introducing the idea of using parametric resonance to detect mass change. This method utilizes stability behavior with mass variation as the detection criterion and high sensitivity is expected. This paper presents theoretical and experimental research on nonlinearity effects on the dynamic behavior of a MEMS oscillator, which is the prototype of such a mass sensor. A Duffing equation and a nonlinear Mathieu equation are used to model the behavior of nonlinear harmonic resonance and parametric resonance. Experimental results agree with the theoretical analysis very well. Some bulk equivalent parameters, such as Q factor, cubic stiffness and linear electrostatic stiffness can be estimated by studying the nonlinear behavior. The estimation of the parameters is important for design of the optimal mass sensor. The potential effects of nonlinearity on mass sensor application are discussed.

scholarly journals Dual-Resonator-Based (DRB) and Multiple-Resonator-Based (MRB) MEMS Sensors: A Review

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1361
Author(s):  
Yusi Zhu ◽  
Zhan Zhao ◽  
Zhen Fang ◽  
Lidong Du
Keyword(s):  
State Of The Art ◽  
Environmental Influences ◽  
High Sensitivity ◽  
Small Mass ◽  
The State ◽  
Mems Sensors ◽  
Mass Sensors ◽  
Sensing Applications

Single-resonator-based (SRB) sensors have thrived in many sensing applications. However, they cannot meet the high-sensitivity requirement of future high-end markets such as ultra-small mass sensors and ultra-low accelerometers, and are vulnerable to environmental influences. It is fortunate that the integration of dual or multiple resonators into a sensor has become an effective way to solve such issues. Studies have shown that dual-resonator-based (DRB) and multiple-resonator-based (MRB) MEMS sensors have the ability to reject environmental influences, and their sensitivity is tens or hundreds of times that of SRB sensors. Hence, it is worth understanding the state-of-the-art technology behind DRB and MRB MEMS sensors to promote their application in future high-end markets.

Noise Analysis in Parametric Resonance Based Mass Sensing

2004 ◽  
Author(s):  
Wenhua Zhang ◽  
Kimberly L. Turner
Keyword(s):  
Brownian Motion ◽  
Parametric Resonance ◽  
Noise Analysis ◽  
High Sensitivity ◽  
Johnson Noise ◽  
Mass Sensing ◽  
And Brownian Motion ◽  
Fluctuation Noise ◽  
Potential Applications ◽  
Harmonic Resonance

Mass sensing based on parametric resonance has shown high sensitivity and has many potential applications in chemical and biological sensing. We investigate noise effects on the sensitivity of mass sensing using parametric resonance. Temperature fluctuation noise, Johnson noise, and Brownian motion noise have been considered. Numerical simulation and experimental results show that noise affects the sensitivity of parametric resonance mass sensing in different mechanism from simple harmonic resonance based mass sensor and Brownian motion noise of the micro-oscillator has the major contribution to the frequency uncertainty at the boundary of parametric resonance area and the sensitivity in mass sensing.

scholarly journals Research and Design of High Sensitivity FBAR Micro-mass Sensors

2021 ◽  
Vol 632 ◽  
pp. 042014
Author(s):  
Jiatai Ren ◽  
Hequn Chu ◽  
Yuhui Bai ◽  
Rui Wang ◽  
Pengguang Chen ◽  
...  
Keyword(s):  
High Sensitivity ◽  
Mass Sensors ◽  
Research And Design

A high sensitivity silicon microcantilever based mass sensor

2008 ◽  
Author(s):  
Margarita Narducci ◽  
Eduard Figueras ◽  
Maria Jose Lopez ◽  
Isabel Gracia ◽  
Luis Fonseca ◽  
...  
Keyword(s):  
High Sensitivity ◽  
Mass Sensor

Stability of Sliding in a System Excited by a Rough Moving Surface

1997 ◽  
Vol 119 (4) ◽  
pp. 672-680 ◽  
Author(s):  
E. J. Berger ◽  
C. M. Krousgrill ◽  
F. Sadeghi
Keyword(s):  
Parametric Resonance ◽  
Normal Force ◽  
Surface Velocity ◽  
Force System ◽  
Periodic Surface ◽  
Linearized System ◽  
Friction Curve ◽  
The Stability ◽  
Small Periodic ◽  
Harmonic Resonance

A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.

On the nonlinear performance of a tuned sloshing damper under small amplitude excitation

2019 ◽  
Vol 25 (21-22) ◽  
pp. 2695-2705 ◽  
Author(s):  
Anuja Roy ◽  
Zili Zhang ◽  
Aparna (Dey) Ghosh ◽  
Biswajit Basu
Keyword(s):  
Small Amplitude ◽  
Numerical Study ◽  
Nonlinear Behavior ◽  
Wave Theory ◽  
Small Mass ◽  
Mass Ratio ◽  
Hybrid Testing ◽  
Low Mass ◽  
Low Mass Ratio ◽  
Nonlinear Performance

This paper explores the potential of a tuned sloshing damper (TSD) in the control of small amplitude vibrations, which is often important from serviceability considerations, through the use of a relatively small mass ratio of the damper liquid. To investigate the nonlinear behavior of the TSD, real-time hybrid testing is conducted in which a single rectangular tank containing water constitutes the prototype TSD. The structure is modeled as a multi-degree-of-freedom system. Two different base input motions, namely harmonic and synthetically generated broad-banded input, are considered. The sensitivity of the TSD performance to tuning ratio vis-à-vis low mass ratio is studied. The experimental results are compared with those obtained from a numerical study carried out using the shallow water wave theory-based nonlinear, semi-empirical model, for the simulation of the sloshing motion of the TSD liquid (water). Results indicate that in the tuned condition, even with a low mass ratio, the TSD is highly effective in the suppression of the small amplitude vibrations, which is underestimated by the simulation model.

Nonlinear Parametric Resonance for NEMS and MEMS Biosensor Applications

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Nonlinear Behavior ◽  
Electrostatic Actuation ◽  
Mass Detection ◽  
Actuation Frequency ◽  
Electrostatically Actuated ◽  
Biosensor Applications

This paper deals with electrostatically actuated resonator micro- and nano-sensor for mass detection for applications in medicine and biology. Nonlinear parametric resonance of the sensor when the electrostatic actuation frequency is near natural frequency of the system is investigated. Mass deposition is included and its effect on the nonlinear behavior of the resonator is predicted.

scholarly journals Finite Element Simulation of Dynamic Stability of Plane Free-Surface of a Liquid under Vertical Excitation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Siva Srinivas Kolukula ◽  
P. Chellapandi
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Parametric Resonance ◽  
Linear Equations ◽  
Parametric Instability ◽  
Initial Perturbation ◽  
Mathieu Equation ◽  
External Excitation ◽  
Nonlinear Potential Theory ◽  
Vertical Excitation

When partially filled liquid containers are excited vertically, the plane free-surface of the liquid can be stable or unstable depending on the amplitude and frequency of the external excitation. For some combinations of amplitude and frequency, the free-surface undergoes unbounded motion leading to instability called parametric instability or parametric resonance, and, for few other combinations, the free-surface undergoes bounded stable motion. In parametric resonance, a small initial perturbation on the free-surface can build up unboundedly even for small external excitation, if the excitation acts on the tank for sufficiently long time. In this paper, the stability of the plane free-surface is investigated by numerical simulation. Stability chart for the governing Mathieu equation is plotted analytically using linear equations. Applying fully nonlinear finite element method based on nonlinear potential theory, the response of the plane free-surface is simulated for various cases.

scholarly journals Modeling processes that provide an avalanche of innovation growth

2021 ◽  
Vol 2131 (4) ◽  
pp. 042001
Author(s):  
S Diakonova ◽  
St Artyshchenko ◽  
N Medvedeva ◽  
M Gusev
Keyword(s):  
Mathematical Modeling ◽  
Parametric Resonance ◽  
Economic Activity ◽  
Mathieu Equation ◽  
Modeling Processes ◽  
Accurate Description ◽  
Growth Stages ◽  
Resonance Model ◽  
Innovation Processes ◽  
Over Time

Abstract This paper proposes an addition to Kondratyev’s theory of the emergence of innovations in long cycles. Regularities of the emergence of crisis phenomena and the concept of “avalanche-like growth of innovations” are considered. The study investigated the innovation peaks occurring in the middle of the depression phase, followed by the growth stages of economic activity after a certain period of time. Research has shown that the active emergence of innovations, which we have called the “snowballing growth of innovations,” falls in the middle of the depression phase. The authors investigated and supplemented the theory of the triggering effect of depression, which is similar to the action of the trigger, which results in an “avalanche-like growth of innovations”. To describe the processes associated with resonance and trigger effects, the authors propose to use the parametric resonance model and the Mathieu equation. With the help of mathematical modeling of innovation processes, a more accurate description of the periodic change in the number of innovations over time is possible, namely, the “avalanche-like growth of innovations”.

Numerical Analysis on Mathieu Instability of a Top-Tensioned Riser in a Dry-Tree Semisubmersible

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Hooi-Siang Kang ◽  
Moo Hyun Kim ◽  
Shankar S. Bhat Aramanadka
Keyword(s):  
Dynamic Stability ◽  
Parametric Resonance ◽  
Structural Integrity ◽  
Mathieu Equation ◽  
Stability Diagram ◽  
Stability Assessment ◽  
Dynamic Tension ◽  
Hydrocarbon Production ◽  
Mathieu Instability ◽  
The Stability

Abstract The development of a dry-tree semisubmersible (DTS), a new type offshore hydrocarbon production system, is facing unconventional challenges in the issues of dynamic stability, structural integrity, and parametric resonance. The Mathieu equation is used to assess the dynamic stability of a top-tensioned riser (TTR) in order to prevent the parametric resonance which leads to detrimental effects on structural integrity. The objectives of this paper are to (i) study a Mathieu stability diagram and its coefficients for an assessment of the stability of a TTR, (ii) identify the effects of the dynamic tension variations in the Mathieu stability assessment, and (iii) analyze the stability of the TTR on a DTS, which is equipped with a long-stroke tensioner, by using numerical simulation. The dynamic tension variation in the DTS was identified to induce instability in the TTR. Hence, the Mathieu stability assessment is recommended to be included in an analysis of TTR behaviors in a dry-tree interface of semisubmersibles.

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