Nonlinear Identification of a Capacitive Dual-Backplate MEMS Microphone

2005 ◽  
Author(s):  
Jian Liu ◽  
David T. Martin ◽  
Karthik Kadirvel ◽  
Toshikazu Nishida ◽  
Mark Sheplak ◽  
...  
Keyword(s):  
Nonlinear System Identification ◽  
Nonlinear Least Squares ◽  
Order System ◽  
Multiple Time Scales ◽  
Model Parameters ◽  
Multiple Time ◽  
Element Analysis ◽  
System Parameters ◽  
Lumped Element ◽  
Mems Microphone

This paper presents the nonlinear system identification of model parameters for a capacitive dual-backplate MEMS microphone. System parameters of the microphone are developed by lumped element modeling (LEM) and a governing nonlinear equation is thereafter obtained with coupled mechanical and electrostatic nonlinearities. The approximate solution for a general damped second order system with both quadratic and cubic nonlinearities and a non-zero external step loading is explored by the multiple time scales method. Then nonlinear finite element analysis (FEA) is performed to verify the accuracy of the lumped stiffnesses of the diaphragm. The microphone is characterized and nonlinear least-squares technique is implemented to identify system parameters from experimental data. Finally uncertainty analysis is performed. The experimentally identified natural frequency and nonlinear stiffness parameter fall into their theoretical ranges for a 95% confidence level respectively.

scholarly journals Critical Parameters and Influence on Dynamic Behaviours of Nonlinear Electrostatic Force in a Micromechanical Vibrating Gyroscope

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Shuying Hao ◽  
Yulun Zhu ◽  
Yuhao Song ◽  
Qichang Zhang ◽  
Jingjing Feng ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Bias Voltage ◽  
Electrostatic Force ◽  
Dynamic Performance ◽  
Great Influence ◽  
Critical Parameters ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Element Analysis ◽  
Dc Bias

The electrostatic force nonlinearity caused by fringe effects of the microscale comb will affect the dynamic performance of the micromechanical vibrating gyroscopes (MVGs). In order to reveal the influence mechanism, a class of four-degree-of-freedom (4-DOF) electrostatically driven MVG is considered. The influence of DC bias voltage and comb spacing on the nonlinearity of electrostatic force and the dynamic response of the MVG by using multiple time scales method and numerical simulation are discussed. The results indicate that the electrostatic force nonlinearity causes the system to show stiffness softening. The softening characteristics of the electrostatic force cause the offset of the resonance frequency and a decrease in sensitivity. Although the electrostatic nonlinearity has a great influence on the dynamic behaviour, its influence can be avoided by the reasonable design of the comb spacing and DC bias voltage. There exists a critical value for comb spacing and DC bias voltage. In this paper, determining the critical values is demonstrated by nonlinear dynamics analysis. The results can be supported by the finite element analysis and numerical simulation.

An Experimental Study of Parametrically Excited Cantilever Beam and System Identification of Nonlinear Modes

2003 ◽  
Author(s):  
Timothy A. Doughty ◽  
Patricia Davies ◽  
Anil Bajaj
Keyword(s):  
Steady State ◽  
System Identification ◽  
Nonlinear System Identification ◽  
Single Mode ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Parametrically Excited ◽  
The Third ◽  
Mode Behavior ◽  
Second Mode

The nonlinear response of a parametrically excited cantilevered beam is experimentally investigated and nonlinear system identification techniques are used to generate nonlinear modal models to explain the observed behavior. Three techniques are applied to data from simulation of a nonlinear single-mode model as well as from experiments, for a beam which is excited with stationary harmonic input at nearly twice the frequency of the beam’s second mode. The first technique is based on the continuous-time differential equation model of the system, the second uses relationships generated by the method of harmonic balance, and the third is based on fitting steady-state response data to steady-state amplitude and phase predictions resulting from a multiple time scales analysis. Each approach is successful when applied to identify models from simulation data. For the experimental data obtained from a beam under nominally identical conditions, difficulties with using higher harmonic information lead to the incorporation of nonlinear damping terms and an investigation of two-mode behavior. Simulated two-mode behavior demonstrates how the beam’s third mode, with natural frequency nearly three times the frequency of the second mode, is excited in the physical structure, thus explaining the mismatch between the previous model and experiment at the third harmonic in the beam’s response.

Vibration Analysis of a Shape Memory Oscillator by Harmonic Balance Method Verified Numerically

2019 ◽  
Vol 29 (03) ◽  
pp. 1930007 ◽  
Author(s):  
Rafal Rusinek ◽  
Joanna Rekas ◽  
Krzysztof Kecik
Keyword(s):  
Shape Memory ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
System Parameters ◽  
Irregular Motion

This paper focuses on periodic solutions for a one-degree-of-freedom oscillator with a spring made of shape memory alloy (SMA). However, when periodic solutions are unstable, irregular motion is identified numerically. The shape memory spring is described by a polynomial characteristic in this model. The harmonic balance method (HBM) is employed to find periodic solutions near the primary resonance. The solutions are confronted with results obtained by the multiple time scales method and numerical simulations. Finally, the effect of system parameters and temperature on the system dynamics is discussed.

Nonlinear System Identification of a MEMS Dual-Backplate Capacitance Microphone by Harmonic Balance Method

2005 ◽  
Author(s):  
Jian Liu ◽  
David T. Martin ◽  
Karthik Kadirvel ◽  
Toshikazu Nishida ◽  
Louis N. Cattafesta ◽  
...  
Keyword(s):  
Steady State ◽  
Governing Equation ◽  
Harmonic Balance ◽  
Nonlinear System Identification ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Algebraic Equations ◽  
Nonlinear Identification ◽  
System Parameters ◽  
Mems Microphone

This paper presents the nonlinear identification of system parameters for a capacitive dual-backplate MEMS microphone. First, the microphone is modeled by a single-degree-of-freedom (SDOF) second order differential equation with electrostatic and cubic mechanical nonlinearities. A harmonic balance nonlinear identification approach is then applied to the governing equation to obtain a set of algebraic equations that relate the unknown system parameters to the steady-state response of the microphone under the harmonic excitation. The microphone is experimentally characterized and a nonlinear least-squares technique is implemented to identify the system parameters from experimental data. The experimentally extracted bandwidth of the microphone is over 218 kHz. Finally, numerical simulations of the governing equation are performed, using the identified system parameters, to validate the accuracy of the approximate solution. The differences between the properties of the integrated measured center velocity and simulated center displacement responses in the steady state are less than 1%.

Prediction and Elimination of Subharmonic Resonances in Mechanical Systems With Nonlinear Foundations

1995 ◽  
Author(s):  
Sotirios Natslavas ◽  
Petros Tratskas
Keyword(s):  
Internal Resonance ◽  
Equations Of Motion ◽  
Single Mode ◽  
Harmonic Excitation ◽  
Multiple Time Scales ◽  
Model Parameters ◽  
Multiple Time ◽  
Algebraic Equations ◽  
Existence And Stability ◽  
Mode Response

Abstract In the first part of this work an analysis is presented on the dynamics of a two degree of freedom nonlinear mechanical oscillator. The model consists of a rigid body which rests on a foundation with nonlinear stiffness. This body can exhibit both vertical and rocking motions, which are coupled through the nonlinearities only. In the present study, attention is focused on the response of the system under external harmonic excitation of the vertical translation only, leading to conditions of subharmonic resonance of order three. Also, the model parameters are chosen so that its two linear natural frequencies are almost identical (1:1 internal resonance). For this case, the method of multiple time scales is first applied and a set of four coupled odes is derived, governing the amplitudes and phases of approximate motions of the system. Then, determination of approximate periodic steady state response of the oscillator is reduced to solving a set of four nonlinear algebraic equations. It is shown that besides linear and nonlinear single-mode response, two-mode response is also possible, due to the internal resonance. In addition, the stability of the various single- and two-mode periodic responses of the system is analyzed. In the last part of the work, the analytical findings are verified and complemented by numerical results. The main interest lies on identifying the effect of system parameters on the existence and stability of the predicted motions. The results of this study reveal patterns of appearance of these motions, which provide valuable help in the efforts to eliminate them. Finally, direct integration of the original equations of motion reveals the existence of other more complex motions, which coexist with the analytically predicted motions within the frequency ranges of interest.

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Odor response adaptation in Drosophila—a continuous individualization process

2021 ◽  
Vol 383 (1) ◽  
pp. 143-148
Author(s):  
Shadi Jafari ◽  
Mattias Alenius
Keyword(s):  
Sensory Neurons ◽  
Olfactory System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Olfactory Perception ◽  
Adaptation Mechanisms ◽  
Metabolic States ◽  
The Central Nervous System ◽  
Olfactory Adaptation ◽  
Central Adaptation

AbstractOlfactory perception is very individualized in humans and also in Drosophila. The process that individualize olfaction is adaptation that across multiple time scales and mechanisms shape perception and olfactory-guided behaviors. Olfactory adaptation occurs both in the central nervous system and in the periphery. Central adaptation occurs at the level of the circuits that process olfactory inputs from the periphery where it can integrate inputs from other senses, metabolic states, and stress. We will here focus on the periphery and how the fast, slow, and persistent (lifelong) adaptation mechanisms in the olfactory sensory neurons individualize the Drosophila olfactory system.

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

scholarly journals A multistate model incorporating estimation of excess hazards and multiple time scales

2021 ◽  
Vol 40 (9) ◽  
pp. 2139-2154
Author(s):  
Caroline E. Weibull ◽  
Paul C. Lambert ◽  
Sandra Eloranta ◽  
Therese M. L. Andersson ◽  
Paul W. Dickman ◽  
...  
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multistate Model
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