Silicon Micro-Ring Gyroscopes

2007 ◽  
Author(s):  
Guo-En Chang ◽  
Chia-Ou Chang ◽  
Chan-Shin Chou ◽  
Wen-Tien Chang Chien
Keyword(s):  
Angular Velocity ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Phase Locking ◽  
Variable Coefficients ◽  
Structure Design ◽  
Mode Shapes ◽  
Nodal Displacement ◽  
Out Of Plane ◽  
The Relationship

The aim of this paper is to analysis a single-crystal microring gyroscope. It is found that Si(111) ring is in-plane isotropic but out-of-plane anisotropic, while Si(100) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with variable coefficients. The exact solutions for frequencies and mode shapes are found. It is also found that the degeneracy of frequencies for isotropic ring splits for anisotropic ring. Then structure design and dynamic analysis of silicon resonant micro-ring gyroscope are presented. The perturbation method of multiple scales is used to find the explicit expression for the relationship between input (angular velocity) and output (nodal displacement of the ring). The effectiveness of phase-locking for enhancing the output signal is proved and quantitatively analyzed.

Closed-Form Solutions of Axisymmetrical Transverse Vibrations of Concave Parabolic Thickness Annular Plates

2009 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equation Of Motion ◽  
Mode Shapes ◽  
Partial Differential ◽  
First Order ◽  
Annular Plates ◽  
Transverse Vibrations

This paper deals with transverse vibrations of axisymmetrical annular plates of concave parabolic thickness. A closed-form solution of the partial differential equation of motion is reported. An approach in which both method of multiple scales and method of factorization have been employed is presented. The method of multiple scales is used to reduce the partial differential equation of motion to two simpler partial differential equations that can be analytically solved. The solutions of the two differential equations are two levels of approximation of the exact solution of the problem. Using the factorization method for solving the first differential equation, which is homogeneous and includes a fourth-order spatial-dependent operator and second-order time-dependent operator, the general solution is obtained in terms of hypergeometric functions. The first diferential equation and the second differential equation (nonhomogeneous) along with the given boundary conditions give so-called zero-order and first-order approximations, respectively, of the natural frequencies and mode shapes. Any boundary conditions could be considered. The influence of Poisson’s ratio on the natural frequencies and mode shapes could be further studied using the first-order approximations reported here. This approach can be extended to nonlinear, and/or forced vibrations.

Influence of In-Plane Modes of a Rotor to Brake Noise

2004 ◽  
Author(s):  
Heewook Lee
Keyword(s):  
Opposite Sign ◽  
Frequency Separation ◽  
Mode Shapes ◽  
Complex Eigenvalue ◽  
Root Cause ◽  
Disk Rotation ◽  
Out Of Plane ◽  
Complex Eigenvalue Analysis ◽  
The Relationship ◽  
Brake Noise

In the effort of improving brake noise, recent studies showed increasing encounters with in-plane modes of a rotor for a root cause of a brake noise. Although studies about in-plane modes of a rotor or a disc have been done a lot, a study about the influence of in-plane modes to brake noise has rarely been done. This paper explored the relationship between unstable eigenvalues and rotor mode shapes, focusing on explaining why unstable eigenvalue excited by in-plane modes behaved differently from one caused by out-of-plane modes. Complex eigenvalue analysis was used to assess the instability of a brake corner. This paper showed the way of analytically calculating the sensitivities of unstable eigenvalues about out-of-plane and inplane modes of a rotor. By using the results of sensitivity analysis, it was first discovered that one of the rotor in-plane doublet modes has the opposite sign to the other in the real parts of the sensitivity, and this precludes eliminating the unstable eigenvalues, which are dominated by rotor in-plane modes. However, it was also found that the corresponding unstable eigenvalues could be eliminated if we could separate the frequencies of these modes. Frequency separation of in-plane doublet modes due to disk rotation was examined.

Study the Effect of Tapering on the Nonlinear Behavior of an Exponentially Varying Width Piezoelectric Energy Harvester

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
H. Salmani ◽  
G. H. Rahimi
Keyword(s):  
Energy Harvester ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
High Amplitude ◽  
Mode Shapes ◽  
Geometric Nonlinearities ◽  
Coupled Equations ◽  
Piezoelectric Energy

It has been shown that exponentially tapering the width of a vibration-based piezoelectric energy harvester will result in increasing electric power per mass in a specified frequency. In this paper, a nonlinear solution of an exponentially decreasing width piezoelectric energy harvester is presented. Piezoelectric, inertial, and geometric nonlinearities are included in the presented model, while the exponentially tapered piezoelectric beam's mass normalized mode shapes are utilized in Galerkin discretization. The developed nonlinear coupled equations of motion are solved using method of multiple scales (MMS), and the steady states results are verified by experiment in high amplitude excitation. Finally, the exponentially tapering parameter effect is studied, and it is concluded that the voltage per mass of the energy harvester is improved by tapering at high exciting acceleration amplitudes.

Nonlinear Vibration of Micromachined Resonators With Attached Excitation/Detection Electrostatic Comb-Drives

2008 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Ebrahim Esmailzadeh ◽  
William L. Cleghorn ◽  
James K. Mills
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Effects ◽  
Added Mass ◽  
Orthogonality Condition ◽  
Mode Shapes ◽  
Resonant Structures ◽  
Comb Drives

Micromachined beams are widely used as resonant structures. The electrostatic interdigitated comb-drives are commonly utilized for exciting/detecting the vibration of these resonators. Recent investigations into the analytical model of the resonator have shown that the added mass due to the comb-drive not only alters the natural frequencies of the resonator, but also changes the mode shapes of vibration. In this paper, the analytical model is extended to include the nonlinear effects due to the stretching of the beam. The generalized orthogonality condition along with the method of assumed-modes summation and the method of multiple scales has been used to study the primary and internal resonance of micro-beam resonators.

Grain separation enhanced magnetic coercivity in Pt/Co multilayers.

1993 ◽  
Vol 51 ◽  
pp. 1038-1039 ◽  
Author(s):  
G.A. Bertero ◽  
R. Sinclair
Keyword(s):  
Remanent Magnetization ◽  
Strong Influence ◽  
Uniaxial Anisotropy ◽  
Magnetic Coupling ◽  
Recording Media ◽  
Magnetic Media ◽  
Signal To Noise ◽  
Out Of Plane ◽  
Longitudinal Recording ◽  
The Relationship

Pt/Co multilayers displaying perpendicular (out-of-plane) magnetic anisotropy and 100% perpendicular remanent magnetization are strong candidates as magnetic media for the next generation of magneto-optic recording devices. The magnetic coercivity, Hc, and uniaxial anisotropy energy, Ku, are two important materials parameters, among others, in the quest to achieving higher recording densities with acceptable signal to noise ratios (SNR). The relationship between Ku and Hc in these films is not a simple one since features such as grain boundaries, for example, can have a strong influence on Hc but affect Ku only in a secondary manner. In this regard grain boundary separation provides a way to minimize the grain-to-grain magnetic coupling which is known to result in larger coercivities and improved SNR as has been discussed extensively in the literature for conventional longitudinal recording media.We present here results from the deposition of two Pt/Co/Tb multilayers (A and B) which show significant differences in their coercive fields.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

SCORING THE JOURNEY: LISTENING TO CLAUDIA MOLITOR'S SONORAMA

Tempo ◽  
2021 ◽  
Vol 76 (299) ◽  
pp. 44-56
Author(s):  
Jonathan Packham
Keyword(s):  
Multiple Scales ◽  
Political Agenda ◽  
The Political ◽  
Refugee Crisis ◽  
Site Specific ◽  
Sharp Focus ◽  
Specific Composition ◽  
Audio Files ◽  
Graphic Score ◽  
The Relationship

AbstractSonorama is a 2015 sonic artwork by Claudia Molitor, consisting of a number of audio files designed for listening on a train journey between London St Pancras and Margate, and a graphic score based on the composer's own ‘reading’ of this journey. This article analyses the relationship between the sonic and the spatial in the work, exploring how Molitor's site-specific composition interacts with its environment on multiple scales. By drawing on the strategy of ‘situated listening’ developed by Gascia Ouzounian, as well as urbanist language introduced by Richard Sennett, this article seeks to elucidate the relationship between a number of ‘nested’ spaces, present across varying realisations, and the political agenda that energises the work. Written in the midst of summer 2015's European refugee crisis, the work brings into sharp focus themes of British exceptionalism, immigration and inclusion.

scholarly journals Dynamic analysis of a parametrically excited golden Muga silk embedded pneumatic artificial muscle

2018 ◽  
Vol 211 ◽  
pp. 02008 ◽  
Author(s):  
Bhaben Kalita ◽  
S. K. Dwivedy
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Quadratic Function ◽  
Artificial Muscle ◽  
Equation Of Motion ◽  
Time Response ◽  
Phase Portraits ◽  
Pneumatic Artificial Muscle ◽  
Pneumatic Muscle

In this work a novel pneumatic artificial muscle is fabricated using golden muga silk and silicon rubber. It is assumed that the muscle force is a quadratic function of pressure. Here a single degree of freedom system is considered where a mass is supported by a spring-damper-and pneumatically actuated muscle. While the spring-mass damper is a passive system, the addition of pneumatic muscle makes the system active. The dynamic analysis of this system is carried out by developing the equation of motion which contains multi-frequency excitations with both forced and parametric excitations. Using method of multiple scales the reduced equations are developed for simple and principal parametric resonance conditions. The time response obtained using method of multiple scales have been compared with those obtained by solving the original equation of motion numerically. Using both time response and phase portraits, variation of few systems parameters have been carried out. This work may find application in developing wearable device and robotic device for rehabilitation purpose.

scholarly journals Self-efficacy as a mediator of the relationship between subjective well-being and general health of military cadets

2014 ◽  
Vol 30 (11) ◽  
pp. 2309-2319 ◽  
Author(s):  
Luciane Albuquerque Sá de Souza ◽  
Ana Raquel Rosas Torres ◽  
Genário Alves Barbosa ◽  
Tiago Jessé Souza de Lima ◽  
Luana Elayne Cunha de Souza
Keyword(s):  
Self Efficacy ◽  
General Health ◽  
Professional Training ◽  
Multiple Scales ◽  
Well Being ◽  
Subjective Well Being ◽  
Mediation Analyses ◽  
The Relationship ◽  
General Self Efficacy

The objective of this study is to investigate the role of self-efficacy beliefs as a mediator of the relationship between the subjective well-being and general health of military cadets (police and firefighters). For this study, 228 cadets participated, the majority being Military Police officer candidates (65%), male (79%), between 17 and 34 years of age (99%), and unmarried (74%). They responded to questionnaires on general health (GHQ-12), perceived general self-efficacy, to the multiple scales that cover subjective well-being, and demographic questions. Initial regression analyses indicate the predictive power of subject well-being regarding general health. Subsequently, the mediation analyses provide satisfactory evidence for the role of perceived self-efficacy as a mediator of the relationship between the subjective well-being variables and the overall health of military cadets. The implications of these results for the professional training of the cadets are discussed.

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