scholarly journals Perturbation Solution for Four-Stream Infrared Radiative Transfer

2020 ◽  
Vol 77 (4) ◽  
pp. 1497-1507
Author(s):  
Jiangnan Li ◽  
Howard W. Barker
Keyword(s):  
Radiative Transfer ◽  
Perturbation Method ◽  
Zero Order ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Dual Wavelength ◽  
Perturbation Equation ◽  
First Order ◽  
Using Data ◽  
First Order Perturbation

Abstract A four-stream solution of the longwave radiative transfer is proposed. It is based on the exact perturbation method utilizing the absorption approximation equation as the zero-order solution. Scattering is handled by the first-order perturbation equation. The two- and four-stream approximations are compared both offline and using data from CALIPSO’s dual-wavelength lidar.

Eigendesign in brake carriers

2013 ◽  
Vol 228 (2) ◽  
pp. 271-280
Author(s):  
Josu Aguirrebeitia ◽  
Joseba Albizuri ◽  
Begoña Martín ◽  
Ander Pol
Keyword(s):  
Perturbation Method ◽  
Manufacturing Process ◽  
Order Perturbation ◽  
First Order ◽  
First Order Perturbation

This work presents the application of a first-order perturbation method to evaluate the eigensensitivity of brake carriers when local geometric alterations arise. This method can be applied both to establish dynamic acceptance conditions of manufacturing-related errors (concept of ‘eigenacceptance’) and to assess the variation of eigenfrequencies and eigenmodes when design variations are done (concept of ‘eigendesign’). As an application of the first concept, the adequacy of the proposed method has been tested in the eigensensitivity of the rest of ingate caused by the manufacturing process; and with regard to the eigendesign concept, an easy-to-use methodology for the redesign of brake carriers has been developed and correlated.

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

2006 ◽  
Vol 06 (03) ◽  
pp. 333-358 ◽  
Author(s):  
B. W. SCHAFER ◽  
L. GRAHAM-BRADY
Keyword(s):  
Monte Carlo ◽  
Perturbation Method ◽  
Perturbation Expansion ◽  
Random Variable ◽  
Order Perturbation ◽  
Initial Slope ◽  
First Order ◽  
Post Buckling ◽  
The Impact ◽  
First Order Perturbation

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

Externally Pressurized Gas Journal Bearings With Porous Inserts

1980 ◽  
Vol 102 (1) ◽  
pp. 113-116 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Eccentricity Ratio ◽  
First Order ◽  
First Order Perturbation

An analytical solution of externally pressurized gas journal bearings with porous inserts as restrictors is presented. The solution is based on a first-order perturbation method with respect to eccentricity ratio.

An Improved Analytical Solution for Self-Acting, Gas-Lubricated Journal Bearings of Finite Length

1961 ◽  
Vol 83 (2) ◽  
pp. 188-192 ◽  
Author(s):  
J. S. Ausman
Keyword(s):  
Analytical Solution ◽  
Finite Length ◽  
Load Capacity ◽  
Journal Bearings ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Small Eccentricity ◽  
First Order ◽  
Bearing Load ◽  
First Order Perturbation

An improved analytical solution designated the “linearized ph” solution is obtained for gas-lubricated journal bearings of finite length. Whereas the older first-order perturbation solution is useful for small eccentricity ratios (ε < 1/2), the linearized ph solution may be used for high eccentricity ratios. As such it permits estimation of ultimate bearing load capacity. The linearized ph solution is expressed in the form of simple corrections to the first-order perturbation solution, and as such can be computed quickly and easily.

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