A Study of Noise Impact on the Stability of Electrostatic MEMS

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Yan Qiao ◽  
Wei Xu ◽  
Hongxia Zhang ◽  
Qin Guo ◽  
Eihab Abdel-Rahman
Keyword(s):  
Noise Intensity ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Low Noise ◽  
Intensity Level ◽  
Lumped Mass ◽  
Mass Model ◽  
Restoring Force ◽  
Electrostatic Mems ◽  
The Stability

Abstract Noise-induced motions are a significant source of uncertainty in the response of micro-electromechanical systems (MEMS). This is particularly the case for electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and drastic loss of stability. This paper investigates the effects of noise processes on the stability of electrostatic MEMS via a lumped-mass model that accounts for uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude. We evaluated the stationary probability density function (PDF) of the resonator response and its basins of attraction in the presence noise and compared them to that those obtained under deterministic excitations only. We found that the presence of noise was most significant in the vicinity of resonance. Even low noise intensity levels caused stochastic jumps between co-existing orbits away from bifurcation points. Moderate noise intensity levels were found to destroy the basins of attraction of the larger orbits. Higher noise intensity levels were found to destroy the basins of attraction of smaller orbits, dominate the dynamic response, and occasionally lead to pull-in. The probabilities of pull-in of the resonator under different noise intensity level are calculated, which are sensitive to the initial conditions.

scholarly journals Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Zhou ◽  
Na Zhao ◽  
Tong Chu ◽  
Ying-Xiang Chang
Keyword(s):  
Joint Venture ◽  
Fractal Structure ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Mixed Duopoly ◽  
Formation Mechanisms ◽  
Multiple Attractors ◽  
Homogeneous Product ◽  
The Stability

In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.

The Existence and Stability of Ultraharmonics and Subharmonics in Forced Nonlinear Oscillations

1954 ◽  
Vol 21 (4) ◽  
pp. 327-335
Author(s):  
T. K. Caughey
Keyword(s):  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Forced Oscillations ◽  
Order System ◽  
Response Curves ◽  
Restoring Force ◽  
Amplitude Frequency Response ◽  
Existence And Stability ◽  
Linearized Theory ◽  
The Stability

Abstract A study is made of the forced oscillations of a second-order system having a small cubic nonlinearity in the restoring force. It is shown that under suitable conditions ultraharmonic or subharmonic motion exists in addition to the harmonic motion which a linearized theory would predict. By studying the stability of such motions it is shown that at points on the amplitude frequency-response curves having vertical tangents, instability and consequently “jumps” occur. A study of the dependence of the motion on the initial conditions reveals that while ultra-harmonic and harmonic motions are rather insensitive to initial conditions, the existence of subharmonic motion can be achieved only for a restricted set of initial conditions.

An Insight into the Analytical Models of Granular Particle Damping

2013 ◽  
Vol 819 ◽  
pp. 13-19
Author(s):  
D.Q. Wang ◽  
C.J. Wu ◽  
R.C. Yang
Keyword(s):  
Analytical Models ◽  
Lumped Mass ◽  
Mass Model ◽  
Complex Particle ◽  
Granular Particle ◽  
Particle Damping ◽  
Particle Dampers ◽  
The Stability ◽  
Improved Model ◽  
The Impact

Granular particle damping technique is a means for achieving high structural damping by the use of metal particles filled into an enclosure which is attached to the structure in a region of high vibration levels. The particle dampers are now preferred over traditional dampers due to the stability, robustness, cost effectiveness and the lower noise level than the impact damper. Such a promising technique has been used successfully in many fields over the past 20 years. In this paper, a state-of-art review on the development of modeling for particle damping is presented. The fundamentals and individual features of three main mathematical models of the granular particle damping are briefly summarized, i.e. the lumped mass model, the Discrete Element Method (DEM) and the approach based on the multiphase flow (MPF) theory of gas-particle. It is worth noting that an improved analytical model of the particle damping based on MPF theory is also introduced. The co-simulation of the COMSOL Multiphysics live link for MATLAB is conducted using this improved model. It can be shown that this model makes the complicated modeling problem more simply and offers the possibility to analyze the more complex particle-damping vibrating system.

The Effects of Nonlinearity on Parametric Amplifiers

2008 ◽  
Author(s):  
Jeffrey F. Rhoads ◽  
Steven W. Shaw
Keyword(s):  
Performance Metrics ◽  
Dynamic Range ◽  
Noise Signal ◽  
Low Noise ◽  
Nonlinear Frequency ◽  
Parametric Amplifiers ◽  
Lumped Mass ◽  
Mass Model ◽  
Nonlinear Frequency Response ◽  
On Chip

Mechanical and electromechanical parametric amplifiers have garnered significant interest, as of late, due to the increased need for low-noise signal amplification in resonant micro/nanosystems. While these devices, which are traditionally designed to operate in a linear range, potentially represent an elegant, on-chip amplification solution, it is not readily apparent that this technical approach will suffice in all micro/nanoresonator implementations, due to the scale-dependent nature of a mechanical or electromechanical amplifier’s dynamic range. The present work investigates whether the aforementioned linear dynamic range constraint is truly a practical limitation, by considering the behavior of a representative degenerate parametric amplifier driven within a nonlinear frequency response regime. The work adopts a comparatively simple lumped-mass model for analysis and proceeds with the characterization of pertinent performance metrics, including gain/pump and gain/phase behaviors. Ultimately, the work concludes that parametric amplification can be realized in a nonlinear context, but such implementations generally lead to inferior amplifier performance.

Multistability in a Simplified Underwater Supercavity System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750121 ◽  
Author(s):  
Yipin Lv ◽  
Tianhong Xiong ◽  
Wenjun Yi
Keyword(s):  
Feedback Control ◽  
Deflection Angle ◽  
Initial Conditions ◽  
Major Change ◽  
Basins Of Attraction ◽  
Cavitation Number ◽  
Stable Equilibrium Point ◽  
Periodic Attractor ◽  
Control Gain ◽  
The Stability

Supercavity can increase the velocity of underwater vehicles greatly, however the launching state of vehicle and systematic parameters often lead to unstable motion. To solve the problem, the effect of parameters and initial conditions on the stability of vehicles is studied. With two variable parameters, namely cavitation number and feedback control gain of fin deflection angle, a simple dynamic model of supercavity system is studied. The multistability is verified through simulation. Robustness of the system is also analyzed based on its basins of attraction. There are various coexisting attractors in a relatively large region of parameter space of the supercavity system, namely coexistence of a stable equilibrium point and a periodic attractor, coexistence of various periodic attractors, coexistence of a periodic attractor with a chaotic attractor and so on, which explain the effect of parameters and initial values on stability of vehicles qualitatively. In addition, without major change in cavitation number, there is a negative correlation between the robustness of the vehicle and feedback control gain of fin deflection angle. The robustness can be improved through optimization of parameters.

Stability Analysis of Electrostatically Actuated Resonators With Delayed Feedback Controller

2010 ◽  
Author(s):  
Fadi Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Initial Conditions ◽  
Basin Of Attraction ◽  
Capacitive Sensor ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Electrostatic Mems ◽  
Delayed Feedback Controller ◽  
The Stability

In this work we investigate the stability of parallel-plate electrostatic MEMS resonators using a delayed feedback controller. Two case studies are investigated: a capacitive sensor made of cantilever beams with a proof mass at their tip and a clamped-clamped microbeam. Dover-cliff integrity curves and basin-of-attraction analysis are used for the stability assessment of the frequency response of the resonators for several scenarios of positive and negative gain in the controller. It is found that, in the case of a positive gain, a velocity or a displacement feedback controller can be used to effectively enhance the stability of the resonators. This is confirmed by an increase in the area of the safe basin of attraction and in shifting the Dover-cliff curve upward. On the other hand, it is shown that a negative gain can significantly weaken the stability of the resonators. This can be of useful use in MEMS for actuation applications, such as in the case of capacitive switches, to lower the activation voltage of these devices and to ensure their trigger under all initial conditions.

Choice and Exchange of Lubricating Oil for Injection Molding Machine

2019 ◽  
Vol 12 (4) ◽  
pp. 378-382
Author(s):  
Shan Syedhidayat ◽  
Quan Wang ◽  
Al-Hadad M.A.A. Mohsen ◽  
Jinrong Wang
Keyword(s):  
Injection Molding ◽  
Dimensional Accuracy ◽  
Low Noise ◽  
Working Environment ◽  
Lubricating Oil ◽  
Lubrication System ◽  
Molding Machine ◽  
Oil And Grease ◽  
Injection Molding Machine ◽  
The Stability

Background: One of the most common manufacturing equipment for polymer product is injection molding machine. In order to ensure the precise, stable and continuous operation of the injection molding machine, the maintenance of the lubrication system must be done well. The stability, reliability, rationality and low noise performance of the lubrication system of injection molding machine directly affect the quality of injection products, dimensional accuracy, molding cycle, working environment and maintenance. Objective: The purpose of this study is to introduce the methods of choice, maintenance of lubricating oil for injection molding machine from many literatures and patents in the recent years, such as lubricating oil device, lubricating composite and structure. Methods: An example of the 260M5 automatic injection molding machine is introduced for the inspection and maintenance of the lubrication system including lubricating oil and lubricating grease. Results: To ensure the lubrication of the injection molding machine, it needs to strictly observe the lubrication time and modulus of the injection molding machine. It needs to strictly control the temperature rise of the lubricating oil and select the correct lubricating oil and grease to ensure the lubrication quality. Conclusion: In the operation of the injection molding machine, it is necessary to check that the lubricating oil is sufficient and the lubricating points are working properly. It ensures sufficient lubrication of the injection molding machine and strictly observes the lubrication time and modulus of the injection molding machine. The stored lubricating oil should be sealed well to prevent air pollution.

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

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