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.

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.

Modeling Geometric Nonlinearities in the Free Vibration of a Planar Beam Flexure With a Tip Mass

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Hamid Moeenfard ◽  
Shorya Awtar
Keyword(s):  
Differential Equations ◽  
Perturbation Technique ◽  
Dynamic Performance ◽  
Nonlinear Partial Differential Equations ◽  
Computational Time ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Analytical Technique ◽  
Numerical Solution Methods ◽  
Tip Mass

The objective of this work is to analytically study the nonlinear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton's principle is utilized to derive the equations governing the nonlinear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these nonlinear partial differential equations are reduced to two coupled nonlinear ordinary differential equations. These equations are solved analytically using the multiple time scales perturbation technique. Parametric analytical expressions are presented for the time domain response of the beam around and far from its internal resonance state. These analytical results are compared with numerical ones to validate the accuracy of the proposed analytical model. Compared with numerical solution methods, the proposed analytical technique shortens the computational time, offers design insights, and provides a broader framework for modeling more complex flexure mechanisms. The qualitative and quantitative knowledge resulting from this effort is expected to enable the analysis, optimization, and synthesis of flexure mechanisms for improved dynamic performance.

Modal Analysis of Boring and Milling Machine

2011 ◽  
Vol 105-107 ◽  
pp. 204-207
Author(s):  
Jian Dong Shang ◽  
Jun Qi Guo ◽  
Dong Fang Hu
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Great Influence ◽  
Element Model ◽  
Mode Shapes ◽  
Machining Accuracy ◽  
Element Analysis ◽  
Modes Of Processing

The vibration is a high-precision machine tool components in the design of the major issues, facing its precision has a great influence, so column parts of its modal analysis is necessary. Creating three-dimensional finite element model of the column, using finite element analysis software ANSYS modal analysis of the column, which can reached the first five natural frequencies and mode shapes. Column Part of our understanding of dynamic performance and improve the machining accuracy is helpful. Modal analysis method is the dynamic performance of the column on the main approach, which mainly is to determine the vibration characteristics of the column that is the natural frequency and vibration mode, which we can determine the modes of processing accuracy, and thus the relevant parts of the machine column can be optimized so that it meet the requirements.

Dynamic Modal Analysis of CNC Precision Rotary Worktable

2011 ◽  
Vol 179-180 ◽  
pp. 787-792
Author(s):  
Qiang Cheng ◽  
Dong Sheng Xuan ◽  
Zhi Feng Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Performance ◽  
Great Influence ◽  
Numerical Control ◽  
Vibration Test ◽  
Element Analysis ◽  
Machining Quality ◽  
Domestic Machine ◽  
Simulation Parameters

The dynamic performance of the worktable has a great influence on machining quality. In order to improve the machining precision, the paper conducts the analysis and research on the workability of a numerical control engine bed rotary worktable from a domestic machine tool factory，and discusses the influence of dynamic characteristics of rotary worktable on the precision of numerical control processing. Firstly Ansys finite element analysis was employed to analyze and simulate the modality and natural frequency of the numerical control rotary worktable under various steps. And then, a vibration test on the numerical control rotary worktable to confirm accuracy of the simulation parameters was carried on. Finally a contrast was made between the theoretical analysis and the experimental analysis to point out the resonance frequency and the distortion of the rotary worktable. Also the influence of numerical control rotary worktable on the numerical control processing was discussed.

Structural Modal Multifurcation With International Resonance: Part 1—Deterministic Approach

1993 ◽  
Vol 115 (2) ◽  
pp. 182-192 ◽  
Author(s):  
R. A. Ibrahim ◽  
A. A. Afaneh ◽  
B. H. Lee
Keyword(s):  
Numerical Simulation ◽  
Fourth Order ◽  
Internal Resonance ◽  
Experimental Testing ◽  
Multiple Time Scales ◽  
Small Range ◽  
Multiple Time ◽  
The Third ◽  
Nonstationary Response ◽  
Detuning Parameter

The bifurcation and multifurcation in multimode interaction of nonlinear continuous structural systems is investigated. Under harmonic excitation the nonstationary response of multimode interaction is considered in the neighborhood of fourth-order internal resonance condition. The response dynamic characteristics are examined via three different approaches. These are the multiple scales method, numerical simulation, and experimental testing. The model considered is a clamped-clamped beam with initial static axial load. Under certain values of the static load the first three normal modes are nonlinearly coupled and this coupling results in a fourth-order internal resonance. The method of multiple time scales yields nonstationary response in the neighborhood of internal resonance. Within a small range of internal detuning parameter the third mode, which is externally excited, is found to transfer energy to the first two modes. Outside this region, the response is governed by a unimodal response of the third mode which follows the Duffing oscillator characteristics. The bifurcation diagram which represents the boundaries that separate unimodal and mixed mode responses is obtained in terms of the excitation level, damping ratios, and internal resonance detuning parameter. The domains of attraction of the two response regimes are also obtained. The numerical simulation of the original equations of motion suggested the occurrence of complex response characteristics for certain values of damping ratios and excitation amplitude. Both numerical integration and experimental results reveal the occurrence of multifurcation as reflected by multi-maxima of the response probability density curves.

Modeling Geometric Non-Linearities in the Free Vibration of a Planar Beam Flexure With a Tip Mass

2012 ◽  
Author(s):  
Hamid Moeenfard ◽  
Shorya Awtar
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Dynamic Performance ◽  
Single Mode ◽  
Resonance State ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Tip Mass

The objective of this work is to create an analytical framework to study the non-linear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton’s principal is utilized to derive the equations governing the non-linear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to two coupled non-linear ordinary differential equations. These equations are solved analytically using combination of the method of multiple time scales and homotopy perturbation analysis. Closed-form, parametric analytical expressions are presented for the time domain response of the beam around and far from its internal resonance state. These analytical results are compared with numerical ones to validate the accuracy of the proposed closed-form model. We expect that the qualitative and quantitative knowledge resulting from this effort will ultimately allow the analysis, optimization, and synthesis of flexure mechanisms for improved dynamic performance.

Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

2017 ◽  
Vol 45 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Alexey Mazin ◽  
Alexander Kapustin ◽  
Mikhail Soloviev ◽  
Alexander Karanets
Keyword(s):  
Numerical Simulation ◽  
Design Optimization ◽  
Strain Tensor ◽  
General Purpose ◽  
Orthogonal Functions ◽  
Element Analysis ◽  
Time Investment ◽  
Footprint Analysis ◽  
Composition Properties ◽  
Nonlinear Elastic

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

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.

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