Distortion of a Harmonic Elastic Wave Reflected From a Dry Friction Support

1998 ◽  
Vol 65 (4) ◽  
pp. 851-857 ◽  
Author(s):  
M. J. Leamy ◽  
J. R. Barber ◽  
N. C. Perkins
Keyword(s):  
Dynamic Response ◽  
Dimensionless Parameter ◽  
Frictional Contact ◽  
Closed Form Solution ◽  
Form Solution ◽  
Harmonic Waves ◽  
Static Stretching ◽  
Belt Drives ◽  
Wide Range ◽  
Range Of Values

This study is motivated by the need to understand the elastodynamic response of belts in frictional contact with pulleys. To this end, a simplified model for belt/pulley contact is used to investigate the dynamic response of a belt subject to a train of harmonic tension waves. Through a nondimensionalization, a single dimensionless parameter Ω is identified which governs the dynamic response. A numerical solution is developed and exercised over a wide range of values of Ω An approximate closed-form solution is derived assuming the belt stretches quasi-statically, and is shown to yield accurate results for small values of Ω Reported results include the distortion of an initially harmonic tension wave, the energy reflected from the frictional support, and the distance harmonic waves penetrate into the support. The results suggest that the quasi-static stretching assumption may be further utilized as a modeling simplification for belt drives characterized by values of Ω <1/3.

The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

Predicting Equation of Transient Position-Probability Density for Nano-Tunnel Problem in SET

2013 ◽  
Vol 284-287 ◽  
pp. 2570-2574
Author(s):  
Sheam Chyun Lin ◽  
Hsien Chang Shih
Keyword(s):  
Probability Density ◽  
Dimensionless Parameter ◽  
Error Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Single Electron ◽  
Analytic Investigation ◽  
Similarity Parameter ◽  
Set Up ◽  
Position Probability

This analytic investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is the most important component in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the PDE equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, appropriate initial and the boundary conditions are set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. In conclusions, this is an innovative approach by using the Schrödinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0≤η≤2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials

2012 ◽  
Vol 28 (2) ◽  
pp. 365-372 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Dynamic Response ◽  
Closed Form ◽  
Fluid Model ◽  
Closed Form Solution ◽  
Mean Value ◽  
Form Solution ◽  
Stochastic Dynamic ◽  
Viscoelastic Materials ◽  
Viscoelastic Modeling ◽  
Nonlinear Fluid

AbstractIn the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

Analysis and Synthesis of Dynamic Response of a Flexibly Coupled Rotor Assembly

1997 ◽  
Author(s):  
Valdas Chaika
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Response ◽  
Wide Range ◽  
Analysis And Synthesis ◽  
Coupling Parameters ◽  
Elastic Couplings ◽  
Rotor Assembly

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.

Quickwave: An Impulse Algorithm to Calculate Preliminary Design Shear and Moment Envelopes for Compliant Towers

1995 ◽  
Vol 117 (2) ◽  
pp. 85-90 ◽  
Author(s):  
D. G. Morrison
Keyword(s):  
Dynamic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Steel Grade ◽  
Preliminary Design ◽  
Wave Load ◽  
Simple Method ◽  
Compliant Tower ◽  
Computer Analyses ◽  
Water Depths

A novel, simple method to calculate compliant tower (CT) level shear and moment envelopes for preliminary design has been developed, and verified by comparing with rigorous 3-D tower analyses. The approach relies on a vast experience base to define important features influencing the dynamic response of CTs, and a new closed-form solution for the acceleration (needed to construct design envelopes) of the tower caused by an impulsive-type wave load. The main benefits of the approach are: 1) the designer can iterate and quickly converge on a working preliminary design without resorting to time-consuming computer analyses; 2) the designer can quickly evaluate configurations for different water depths, pile arrangements, payload, steel grade, reserve buoyancy, and well counts.

Gyroscopic and Support Effects on the Steady-State Response of a Noncontacting Flexibly Mounted Rotor Mechanical Face Seal

1989 ◽  
Vol 111 (2) ◽  
pp. 200-206 ◽  
Author(s):  
I. Green
Keyword(s):  
Dynamic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Steady State Response ◽  
Face Seal ◽  
State Response ◽  
High Speeds ◽  
Relative Response ◽  
Mechanical Face Seal ◽  
Stiffness And Damping

The dynamic behavior of a noncontacting rotary mechanical face seal is analyzed. A closed-form solution is presented for the response of a flexibly mounted rotor to forcing misalignments which normally exist due to manufacturing and assembly tolerances. The relative misalignment between the rotor and the stator, which is the most important seal parameter, has been found to be time dependent with a cyclically varying magnitude. The relative response is minimum when support stiffness and damping are minimum. The gyroscopic couple is shown to have a direct effect on the dynamic response. This effect is enhanced at high speeds, and depending on the ratio between the transverse and polar moments of inertia, it can either decrease or increase the dynamic response. Its effect is most beneficial to seal performance when the rotor is a “short disk.” A numerical example demonstrates that a flexibly-mounted rotor seal outperforms a flexibly mounted stator seal with regard to the total relative misalignment, the critical stator misalignment, and the critical speed.

scholarly journals Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

2016 ◽  
Vol 113 (40) ◽  
pp. 11220-11225 ◽  
Author(s):  
Ramu Anandakrishnan ◽  
Zining Zhang ◽  
Rory Donovan-Maiye ◽  
Daniel M. Zuckerman
Keyword(s):  
Closed Form Solution ◽  
Atp Synthesis ◽  
Form Solution ◽  
Energy Conditions ◽  
Rotary Machine ◽  
Wide Range ◽  
Steady State Rate ◽  
Systematic Enumeration ◽  
Kinetic Effects ◽  
Chemical Cycle

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated “kinetic equivalence” of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Estimation of Stress Intensity Factor for Circumferential Through-Wall Cracked Elbows Subjected to In-Plane Bending

2015 ◽  
Author(s):  
Han-Bum Surh ◽  
Jong Wook Kim ◽  
Min Kyu Kim ◽  
Min-Gu Won ◽  
Moon Ki Kim ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Form Solution ◽  
Accurate Estimation ◽  
Wide Range ◽  
Plane Bending ◽  
Geometric Variables

The stress intensity factor (SIF) is the major fracture mechanics parameter in LEFM concept. Since the SIF can be used for not only calculation of J-integral based on the GE/EPRI and reference stress method but also evaluation of fatigue crack growth, an accurate estimation of the SIF is an important issue for the piping in nuclear power plant. Recently, there is a need to develop the SIF solution which can cover wide geometric variables since there are on-going efforts that are developing next generation reactors in Korea, which is designed to thin-walled structures. For the through-wall cracked straight pipes, many researchers have proposed the SIF solutions which can cover wide range of wall thickness. However, since only limited solutions have been proposed yet for the through-wall cracked elbows, a research related to the SIF estimation for the elbows with wide geometric variables should be performed. In this study, the extended SIF solution for circumferential through-wall cracked elbows subjected to in-plane bending is proposed as the tabulated form through the finite element (FE) analyses. Wide elbow geometries are selected to range between 5 and 50 of Rm/t and range between 2∼20 of Rb/Rm. The existing solutions are then reviewed by comparing with the FE results. Furthermore, effects of geometric variables on the SIF are addressed through systematic investigation of FE based SIF results. These investigated results are expected to contribute to the development of closed form solution for the circumferential through-wall cracked elbows subjected to in-plane bending.

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