scholarly journals A convergence study for the Laguerre expansion in the moment equation method for neoclassical transport in general toroidal plasmas

2010 ◽  
Vol 17 (8) ◽  
pp. 082510 ◽  
Author(s):  
S. Nishimura ◽  
H. Sugama ◽  
H. Maaßberg ◽  
C. D. Beidler ◽  
S. Murakami ◽  
...  
Keyword(s):  
Moment Equation ◽  
Equation Method ◽  
Laguerre Expansion ◽  
Toroidal Plasmas ◽  
Neoclassical Transport ◽  
Convergence Study ◽  
The Moment

A Generalized Integral Computation Technique for Nonequilibrium Compressible Turbulent Boundary Layers Using Moment Equations

1972 ◽  
Vol 39 (3) ◽  
pp. 667-672 ◽  
Author(s):  
J. P. Lamb ◽  
L. J. Hesler ◽  
J. H. Smith
Keyword(s):  
Boundary Layers ◽  
Mechanical Energy ◽  
Moment Equation ◽  
Turbulent Boundary Layers ◽  
Moment Equations ◽  
Governing Equations ◽  
Starting Conditions ◽  
The Moment ◽  
Momentum Integral ◽  
Layer Concept

Computation of nonequilibrium compressible turbulent boundary layers using Coles’ three-parameter representation for the layer (cf, δ, Π) is discussed. Governing equations include momentum integral, skin friction, and an integral moment equation. It is shown that the hypothetical equilibrium layer concept employed by Alber to determine the dissipation integral of the mechanical energy equation can be utilized to estimate similar auxiliary parameters in the entrainment and moment-of-momentum integral equations. A series of comparisons of experimental data and predictions, using each of the moment equations shows that all combinations yield very similar results which are in general agreement with measurements. Some sensitivity to starting conditions was observed with the moment-of-momentum and entrainment relations.

Evaluation of moment equation in the 2000 Canadian highway bridge design code for soil–metal arch structures

2004 ◽  
Vol 31 (2) ◽  
pp. 281-291 ◽  
Author(s):  
Dong-Ho Choi ◽  
Gi-Nam Kim ◽  
Peter M Byrne
Keyword(s):  
Finite Element ◽  
Moment Equation ◽  
Finite Element Analyses ◽  
Moment Equations ◽  
Metal Structures ◽  
Maximum Moment ◽  
Design Variables ◽  
Arch Structures ◽  
The Moment ◽  
Soil Metal

This paper evaluates the moment equation in the 2000 Canadian highway bridge design code (CHBDC) for soil–metal arch structures. This equation is adopted from Duncan's moment equation (1978), which is based on his finding from finite element analyses that the maximum moment occurs at the quarter point of soil-metal structures. However, finite element analyses carried out for this study demonstrate that the maximum moment in soil–metal arch structures with spans greater than approximately 11 m occurs at the crown point. In this study, the location and magnitude of the maximum moment was examined for soil–metal arch structures having spans of 6–20 m under three construction stages; backfill up to the crown, backfill up to the cover depth, and live loading. Based on the location of the maximum moment, two sets of moment equations dependant on span length were found necessary. Moment coefficients and moment reduction factors in moment equations are proposed from the results of numerous finite element analyses for semi-circular arch and part-arch types of soil–metal structures considering the various design variables, such as span length, structural shapes, section properties, and backfill conditions. The validity of the coefficients and reduction factors in the moment equation of the 2000 CHBDC is investigated by comparison with those proposed in this study. The comparison demonstrates that the moment equation of the 2000 CHBDC is still valid and a little conservative. The effects of design variables on the variations of moments of soil–metal arch structures during construction stages are also examined.Key words: soil–metal arch structures, moment equations, CHBDC, soil-structure interaction.

A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations

2002 ◽  
Vol 124 (4) ◽  
pp. 561-565 ◽  
Author(s):  
O. Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Control Design ◽  
Stochastic Averaging ◽  
Moment Equation ◽  
Design Criteria ◽  
Numerical Examples ◽  
Rayleigh Approximation ◽  
Stochastic Controls ◽  
The Moment

This paper presents a method for designing and quantifying the performance of feedback stochastic controls for nonlinear systems. The design makes use of the method of stochastic averaging to reduce the dimension of the state space and to derive the Ito^ stochastic differential equation for the response amplitude process. The moment equation of the amplitude process closed by the Rayleigh approximation is used as a means to characterize the transient performance of the feedback control. The steady state and transient response of the amplitude process are used as the design criteria for choosing the feedback control gains. Numerical examples are studied to demonstrate the performance of the control.

PARAMETRIC VIBRATION OF STAY CABLES UNDER AXIAL NARROW-BAND STOCHASTIC EXCITATION

2013 ◽  
Vol 13 (08) ◽  
pp. 1350035 ◽  
Author(s):  
MING GU ◽  
SHU-YAN REN
Keyword(s):  
Yangtze River ◽  
Narrow Band ◽  
Moment Equation ◽  
The Yangtze River ◽  
Closed Form Solutions ◽  
Response Characteristics ◽  
Variation Characteristics ◽  
The Moment ◽  
Non Gaussian ◽  
General Response

The differential equation for inclined cables under axial narrow-band stochastic excitations is established with consideration of the cable sag and variations of cable tension along the cable. Gaussian and first-order non-Gaussian closed-form solutions are derived by employing the statistical moment truncation method to solve the moment equation. A long cable (Cable A20 of No. 2 Nanjing Bridge over the Yangtze River) is taken as an example to demonstrate the application of the theoretical model presented. The Monte Carlo method is also adopted to simulate the responses of the cable numerically under investigation. The general response characteristics of the cable are analyzed, particularly, the variation characteristics of the response of the cable depending on the excitation bandwidth when the ratio of the central frequency of excitation to the first frequency of cable is equal to one or two. Parametric vibrations of the real Cable A20 excited by the buffeting vibration of the bridge deck of No. 2 Nanjing Bridge over the Yangtze River are also calculated.

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