scholarly journals Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators

Micromachines ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 614 ◽  
Author(s):  
Jianxin Han ◽  
Lei Li ◽  
Gang Jin ◽  
Wenkui Ma ◽  
Jingjing Feng ◽  
...  
Keyword(s):  
Fundamental Frequency ◽  
Mathematical Proof ◽  
Differential Quadrature Method ◽  
Upper And Lower Bounds ◽  
Physical Parameters ◽  
Theoretical Derivation ◽  
Fundamental Frequencies ◽  
Mems Resonators ◽  
Statics And Dynamics ◽  
Cubic Stiffness

This paper attempts to qualitatively identify the static pull-in position, pull-in voltage, and fundamental frequency of one-electrode microresonators from a physical perspective. During theoretical derivation, a generalized one-degree-of-freedom (1-DOF) model in nondimensional form derived using the differential quadrature method (DQM) is first introduced and then transformed for frequency normalization. Based on the deduced formulas, the upper and lower bounds of the static pull-in position and pull-in voltage are both deduced through mathematical proof. To distinguish the monotonic and nonmonotonic behavior of the fundamental frequency versus direct current (DC) voltage, a critical condition decided only by cubic stiffness is then determined. For the first time, two extreme static positions, as well as the corresponding fundamental frequencies and DC voltages to identify different frequency behaviors are derived, and their variations versus cubic stiffness are then discussed and verified. During the simulation process, a high-order DQM and COMSOL 2D model are both applied for numerical analyses. Guided by nondimensional results, typical behaviors with specific physical parameters are examined in detail. Results demonstrate that the curve tendencies between all the qualitative results and quantitative numerical simulations in dimensional form agree well with each other, implying the possibility of using 1-DOF model to qualitatively discuss physical parameters effects on the system statics and dynamics.

A Tape Striation Counting Method for Determining Fundamental Frequency

1979 ◽  
Vol 10 (4) ◽  
pp. 246-248 ◽  
Author(s):  
Peter B. Mueller ◽  
Marla Adams ◽  
Jean Baehr-Rouse ◽  
Debbie Boos
Keyword(s):  
Fundamental Frequency ◽  
Counting Method ◽  
Male And Female ◽  
Fundamental Frequencies ◽  
Counting Procedure ◽  
Female Subjects

Mean fundamental frequencies of male and female subjects obtained with FLORIDA I and a tape striation counting procedure were compared. The fundamental frequencies obtained with these two methods were similar and it appears that the tape striation counting procedure is a viable, simple, and inexpensive alternative to more costly and complicated procedures and instrumentation.

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

The Influence of Support Hardware and Piping System Seismic Response on Snubber Support Damping

1997 ◽  
Vol 119 (4) ◽  
pp. 451-456 ◽  
Author(s):  
C. Lay ◽  
O. A. Abu-Yasein ◽  
M. A. Pickett ◽  
J. Madia ◽  
S. K. Sinha
Keyword(s):  
Seismic Response ◽  
Fundamental Frequency ◽  
Damping Ratio ◽  
Damping Coefficient ◽  
Piping System ◽  
Nodal Displacement ◽  
Damping Coefficients ◽  
Fundamental Frequencies ◽  
Piping Systems

The damping coefficients and ratios of piping system snubber supports were found to vary logarithmically with pipe support nodal displacement. For piping systems with fundamental frequencies in the range of 0.6 to 6.6 Hz, the support damping ratio for snubber supports was found to increase with increasing fundamental frequency. For 3-kip snubbers, damping coefficient and damping ratio decreased logarithmically with nodal displacement, indicating that the 3-kip snubbers studied behaved essentially as coulomb dampers; while for the 10-kip snubbers studied, damping coefficient and damping ratio increased logarithmically with nodal displacement.

scholarly journals Scaling of separated shear layers: an investigation of mass entrainment

2017 ◽  
Vol 826 ◽  
pp. 851-887 ◽  
Author(s):  
Francesco Stella ◽  
Nicolas Mazellier ◽  
Azeddine Kourta
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Separated Flow ◽  
Layer Growth ◽  
Upper And Lower Bounds ◽  
Stream Velocity ◽  
Physical Parameters ◽  
Separated Shear Layer ◽  
Mass Entrainment ◽  
Recirculation Length

We report an experimental investigation of the separating/reattaching flow over a descending ramp with a $25^{\circ }$ expansion angle. Emphasis is given to mass entrainment through the boundaries of the separated shear layer emanating from the upper edge of the ramp. For this purpose, the turbulent/non-turbulent interface and the separation line inferred from image-based analysis are used respectively to mark the upper and lower bounds of the separated shear layer. The main objective of this study is to identify the physical parameters that scale the development of the separated shear layer, by giving a specific emphasis to the investigation of mass entrainment. Our results emphasise the multiscale nature of mass entrainment through the separated shear layer. The recirculation length $L_{R}$, step height $h$ and free-stream velocity $U_{\infty }$ are the dominant scales that organise the separated flow (and related large-scale quantities as pressure distribution or shear layer growth rate) and set mean mass fluxes. However, local viscous mechanisms seem to be responsible for most of local mass entrainment. Furthermore, it is shown that large-scale mass entrainment is driven by incoming boundary layer properties, since $L_{R}$ scales with $Re_{\unicode[STIX]{x1D703}}$, and in particular by its turbulent state. Surprisingly, the relationships evidenced in this study suggest that these dependencies are established over a large distance upstream of separation and that they might also extend to small scales, at which viscous entrainment is dominant. If confirmed by additional studies, our findings would open new perspectives for designing effective separation control systems.

Phonetics of Singing in Western Classical Style

2018 ◽  
Author(s):  
Johan Sundberg
Keyword(s):  
Fundamental Frequency ◽  
Vocal Fold ◽  
Vocal Tract ◽  
Formant Frequency ◽  
Vowel Identification ◽  
Fundamental Frequencies ◽  
Vocal Fold Vibration ◽  
Syllable Duration ◽  
Classical Singing ◽  
The Voice

The function of the voice organ is basically the same in classical singing as in speech. However, loud orchestral accompaniment has necessitated the use of the voice in an economical way. As a consequence, the vowel sounds tend to deviate considerably from those in speech. Male voices cluster formant three, four, and five, so that a marked peak is produced in spectrum envelope near 3,000 Hz. This helps them to get heard through a loud orchestral accompaniment. They seem to achieve this effect by widening the lower pharynx, which makes the vowels more centralized than in speech. Singers often sing at fundamental frequencies higher than the normal first formant frequency of the vowel in the lyrics. In such cases they raise the first formant frequency so that it gets somewhat higher than the fundamental frequency. This is achieved by reducing the degree of vocal tract constriction or by widening the lip and jaw openings, constricting the vocal tract in the pharyngeal end and widening it in the mouth. These deviations from speech cause difficulties in vowel identification, particularly at high fundamental frequencies. Actually, vowel identification is almost impossible above 700 Hz (pitch F5). Another great difference between vocal sound produced in speech and the classical singing tradition concerns female voices, which need to reduce the timbral differences between voice registers. Females normally speak in modal or chest register, and the transition to falsetto tends to happen somewhere above 350 Hz. The great timbral differences between these registers are avoided by establishing control over the register function, that is, over the vocal fold vibration characteristics, so that seamless transitions are achieved. In many other respects, there are more or less close similarities between speech and singing. Thus, marking phrase structure, emphasizing important events, and emotional coloring are common principles, which may make vocal artists deviate considerably from the score’s nominal description of fundamental frequency and syllable duration.

Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics

2018 ◽  
Vol 10 (04) ◽  
pp. 1850041 ◽  
Author(s):  
Ye Tang ◽  
Tianzhi Yang
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Graded Materials ◽  
Critical Flow Velocity ◽  
Dynamic Behaviors ◽  
Fundamental Frequencies ◽  
Material Gradation

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.

scholarly journals Influence of Physical Parameters and Operating Conditions for Structural Integrity of Mechanical System Subjected to Squeal Noise

2013 ◽  
Vol 569-570 ◽  
pp. 1076-1084 ◽  
Author(s):  
Kevin Soobbarayen ◽  
Sébastien Besset ◽  
Jean Jacques Sinou
Keyword(s):  
Friction Coefficient ◽  
Static Loading ◽  
Structural Integrity ◽  
Operating Conditions ◽  
Brake System ◽  
Physical Parameters ◽  
Loading Conditions ◽  
Fundamental Frequencies ◽  
Loading Case ◽  
Squeal Noise

This work proposes to study the effects of physical parameters and loading conditions on both dynamic and acoustic responses of a brake system subjected to squeal. A simplified brake system model composed of a disc and a pad is investigated. The friction interface is modeled by introducing linear and non-linear stiffnesses at several local nodes to model contact. The classical Coulomb law is applied to model friction and the friction coefficient is assumed to be constant. A stability analysis of this system is performed with respect to the friction coefficient and the hydraulic brake pressure. Then self-excited vibrations are investigated for two cases of loading conditions: static loading and ramp loading. Time responses for these cases are significantly different: the case with ramp loading presents higher amplitude of velocity than the static loading case. For the case with ramp loading, the spectrum analysis performed by the Continuous Wavelet Transform, shows the appearance of the fundamental frequencies of unstable modes but also their harmonics and combinations frequencies. Sound pressures radiated during squeal event present different peculiar patterns of directivity for both cases and for a progressive load, the levels are significantly higher.

Fermi Surface Study of Organic Metals (Bedt-TTF)2X

1992 ◽  
Vol 247 ◽  
Author(s):  
M. Tokumoto ◽  
A. G. Swanson ◽  
J. S. Brooks ◽  
C. C. Agosta ◽  
S. T. Hannahs ◽  
...  
Keyword(s):  
Fermi Surface ◽  
Fundamental Frequency ◽  
Electronic System ◽  
Surface Topology ◽  
Spin Splitting ◽  
Simple Metal ◽  
Organic Metals ◽  
Fundamental Frequencies ◽  
First Time ◽  
Oscillation Characteristic

ABSTRACTObservations of Shubnikov-de Haas(SdH) and de Haas-van Alphen(dHvA) oscillations in organic metals (BEDT-TTF)2X, with X=KHg(SCN)4, θ-I3 and β″-AuBr2. are reported. In KHg(SCN)4 salt, in addition to the SdH oscillations with fundamental frequency of 670 T corresponding to about 16% of the first Brillouin zone(FBZ), we observed splitting of each SdH peak which we ascribed to “spin-splitting” We have also found that the ground state of this salt is not a simple metal but has some magnetic character. In θ-l3 salt we have succeeded in an observation of dHvA oscillations for the first time. We observed a “saw-tooth” dHvA oscillation characteristic to a highly two-dimensional and extraordinary clean electronic system. In addition to the fundamental frequency of 4170 T corresponding to 50.4 % of the FBZ and its higher harmonics, we observed an oscillation with lower frequency of 730 T corresponding to about 8.8 % of the FBZ. A new Fermi surface topology for θ-l3 salt is proposed based on the analysis of the dHvA effect. In β″-AuBr2, we observed complex dHvA oscillations, which can be explained in terms of the mixing of two fundamental frequencies of 47 and 268 T, suggesting the presence of very small pockets corresponding to 0.6 and 2.9 % of the FBZ.

Tailoring the Fundamental Frequency of Laminated Composite Panels Using Material Properties

2014 ◽  
Vol 709 ◽  
pp. 157-161
Author(s):  
Li Guo Zhang ◽  
Kang Yang ◽  
Wei Ping Zhao ◽  
Song Xiang
Keyword(s):  
Fundamental Frequency ◽  
Material Properties ◽  
Present Method ◽  
Optimization Problem ◽  
Laminated Composite ◽  
Composite Panels ◽  
Fundamental Frequencies ◽  
Laminated Panels ◽  
Frequency Optimization ◽  
Optimal Material

Optimization of material properties is performed to maximize the fundamental frequency of the laminated composite panels by means of the genetic algorithm. The global radial basis function collocation method is used to calculate the fundamental frequency of clamped laminated composite panels. In this paper, the objective function of optimization problem is the maximum fundamental frequency; optimization variables are material properties of laminated panels. The results for the optimal material properties and the maximum fundamental frequencies of the 2-layer plates are presented to verify the validity of present method.

Theory of Helmholtz-Beat Frequencies

1984 ◽  
Vol 1 (3) ◽  
pp. 308-322 ◽  
Author(s):  
Rudolf A. Rasch
Keyword(s):  
Fundamental Frequency ◽  
Beat Frequency ◽  
Numerical Data ◽  
Fundamental Frequencies ◽  
The Absolute ◽  
Frequency Ratios

In musical tuning, deviations from the simple frequency ratios of pure consonant intervals are often necessary. These deviations are called temperings. They result in beats in the sounding interval. Rules are developed according to which the beat frequencies can be determined, both exactly and by way of easy integer approximations. Beat frequencies of consonant intervals are most easily expressed as relative beat frequencies, the quotient of the beat frequency and the lower fundamental frequency of the interval. The relative beat frequency is a constant for a certain interval in a certain tuning, whereas the absolute beat frequencies vary with fundamental frequencies. Also described are the relationships between the beat frequencies of the three intervals that make up a consonant triad. Numerical data are given for five model tunings: Pythagorean, equal, Silbermann, meantone, and Salinas.

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