On the Approach to Steady State for Frictional Contact Under Moving Loads

1983 ◽  
Vol 50 (4a) ◽  
pp. 783-788 ◽  
Author(s):  
J. Dundurs ◽  
A. K. Gautesen
Keyword(s):  
Steady State ◽  
Integral Equations ◽  
Frictional Contact ◽  
Moving Loads ◽  
Contact Interface ◽  
Normal Forces ◽  
Approach To Steady State

There is a class of problems involving frictional contact for which a steady state of slip is possible under moving loads as, for instance, when a tire is press-fitted on a wheel, and loaded by forces that travel along its circumference and induce localized slip between the tire and the wheel. The steady state slip has been investigated before, but no estimates showing how quickly the steady state is approached are available. The present paper considers for this purpose a problem that can largely be reduced analytically. It involves two half spaces that are pressed together and sheared. The contact interface is locally pried apart by concentrated normal tractions which, after application, start to move. The moving normal forces induce localized separation and slip zones that travel along the interface. The analysis based on integral equations shows that the approach to steady state is relatively slow.

Unsteady convective exchange flows in cavities

1998 ◽  
Vol 368 ◽  
pp. 127-153 ◽  
Author(s):  
J. J. STURMAN ◽  
G. N. IVEY
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Boundary Layer Thickness ◽  
Buoyancy Flux ◽  
Exchange Flow ◽  
Flushing Time ◽  
Exchange Flows ◽  
Buoyancy Forcing ◽  
Convective Exchange ◽  
Approach To Steady State

Horizontal exchange flows driven by spatial variation of buoyancy fluxes through the water surface are found in a variety of geophysical situations. In all examples of such flows the timescale characterizing the variability of the buoyancy fluxes is important and it can vary greatly in magnitude. In this laboratory study we focus on the effects of this unsteadiness of the buoyancy forcing and its influence on the resulting flushing and circulation processes in a cavity. The experiments described all start with destabilizing forcing of the flows, but the buoyancy fluxes are switched to stabilizing forcing at three different times spanning the major timescales characterizing the resulting cavity-scale flows. For destabilizing forcing, these timescales are the flushing time of the region of forcing, and the filling-box timescale, the time for the cavity-scale flow to reach steady state. When the forcing is stabilizing, the major timescale is the time for the fluid in the exchange flow to pass once through the forcing boundary layer. This too is a measure of the time to reach steady state, but it is generally distinct from the filling-box time. When a switch is made from destabilizing to stabilizing buoyancy flux, inertia is important and affects the approach to steady state of the subsequent flow. Velocities of the discharges from the end regions, whether forced in destabilizing or stabilizing ways, scaled as u∼(Bl)1/3 (where B is the forcing buoyancy flux and l is the length of the forcing region) in accordance with Phillips' (1966) results. Discharges with destabilizing and stabilizing forcing were, respectively, Q−∼(Bl)1/3H and Q+∼(Bl)1/3δ (where H is the depth below or above the forcing plate and δ is the boundary layer thickness). Thus Q−/Q+>O(1) provided H>O(δ), as was certainly the case in the experiments reported, demonstrating the overall importance of the flushing processes occurring during periods of cooling or destabilizing forcing.

Signal strength in subsecond FLASH magnetic resonance imaging: The dynamic approach to steady state

1990 ◽  
Vol 17 (6) ◽  
pp. 1004-1010 ◽  
Author(s):  
W. Hänicke ◽  
K. D. Merboldt ◽  
D. Chien ◽  
M. L. Gyngell ◽  
H. Bruhn ◽  
...  
Keyword(s):  
Magnetic Resonance Imaging ◽  
Steady State ◽  
Magnetic Resonance ◽  
Signal Strength ◽  
Resonance Imaging ◽  
Dynamic Approach ◽  
Approach To Steady State

Numerical Solution of the Planar Hydrostatic Foil Bearing

1979 ◽  
Vol 101 (1) ◽  
pp. 86-91 ◽  
Author(s):  
A. Eshel
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Computer Program ◽  
Numerical Solution ◽  
Asymptotic Approach ◽  
State Problem ◽  
Shooting Technique ◽  
Foil Bearing ◽  
Approach To Steady State ◽  
Steady State Problem

The steady state problem of the planar hydrostatic foil bearing is analyzed and solved numerically. Two techniques of solution are used. One method is simulation in time with asymptotic approach to steady state. This is achieved by a preprocessor which automatically sets up the numerical computer program. The second method is an iterative shooting technique. The results agree well with one another. Curves of pressure and typical film thickness versus flow are presented.

A new approach to steady state analysis of nonlinear electrical circuits

2017 ◽  
Vol 36 (3) ◽  
pp. 716-728 ◽  
Author(s):  
Tadeusz Sobczyk ◽  
Michał Radzik
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
Direct Calculation ◽  
Electrical Circuits ◽  
Steady State Analysis ◽  
Content Type ◽  
The Time Domain ◽  
Approach To Steady State ◽  
State Analysis

Purpose The purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain. Design/methodology/approach An iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants. Findings This study found a novel differential operator for periodic functions and its application in the steady-state analysis. Research limitations/implications This approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems. Practical implications The complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach. Originality/value This study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.

Effects of membrane hardness and scaling analysis for capsules in planar extensional flows

2014 ◽  
Vol 745 ◽  
pp. 487-508 ◽  
Author(s):  
P. Dimitrakopoulos
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Edge Length ◽  
Scaling Analysis ◽  
Normal Forces ◽  
Shearing Resistance ◽  
Slender Spindle ◽  
Physical Insight ◽  
Extensional Flows ◽  
Local Edge

AbstractIn this paper, we investigate computationally the effects of membrane hardness on the dynamics of strain-hardening capsules in planar extensional Stokes flows. As the flow rate increases, all capsules reach elongated steady-state configurations but the cross-section of the more strain-hardening capsules preserves its elliptical shape while the less strain-hardening capsules become lamellar. The capsule deformation in strong extensional flows is accompanied with very pointed edges, i.e. large edge curvatures and thus small local edge length scales, which makes the current investigation a multi-length interfacial dynamics problem. Our computational results for elongated strain-hardening capsules are accompanied with a scaling analysis which provides physical insight on the extensional capsule dynamics. The two distinct capsule conformations we found, i.e. the slender spindle and lamellar capsules, are shown to represent two different types of steady-state extensional dynamics. The former are stabilized mainly via the membrane’s shearing resistance and the latter via its area-dilatation resistance, associated with the elongation tension normal forces and thus both types differ from bubbles which are stabilized mainly via the lateral surface-tension normal forces. Our steady-state deformation results can be used to identify the elastic properties of a real capsule, i.e. the membrane’s shear and area-dilatation moduli, utilizing a single experimental technique.

scholarly journals An Approximate Analytical Approach to Steady State Simulation of Unglazed Solar Collectors

2014 ◽  
Vol 48 ◽  
pp. 28-36 ◽  
Author(s):  
Luigi P.M. Colombo ◽  
Cesare M. Joppolo ◽  
Luca Molinaroli ◽  
Elisa Rovelli
Keyword(s):  
Steady State ◽  
Analytical Approach ◽  
Solar Collectors ◽  
Steady State Simulation ◽  
Approach To Steady State
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