Betatron coupling correction at the IUCF cooler, leading to improved determination of fourth-order resonance Hamiltonian

1992 ◽  
Author(s):  
M. Ellison ◽  
M. Ball ◽  
B. Brabson ◽  
J. Budnick ◽  
D. D. Caussyn ◽  
...  
Keyword(s):  
Fourth Order ◽  
Order Resonance ◽  
Betatron Coupling

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

Fourth Order Derivative Spectrophotometric Determination of Lead with 1,10-Phenanthroline and Rose Bengal

1993 ◽  
Vol 26 (3) ◽  
pp. 523-539 ◽  
Author(s):  
D. Sreevalsan Nair ◽  
T. Prasada Rao ◽  
C. S. P. Iyer ◽  
A. D. Damodaran
Keyword(s):  
Spectrophotometric Determination ◽  
Fourth Order ◽  
Rose Bengal ◽  
Order Derivative

Fluorescent kinetics combined with fourth-order calibration for the determination of diclofenac sodium in environmental water

2019 ◽  
Vol 411 (10) ◽  
pp. 2019-2029 ◽  
Author(s):  
Jiao Li ◽  
Jie Xu ◽  
Wenying Jin ◽  
Zhongsheng Yi ◽  
Chenbo Cai ◽  
...  
Keyword(s):  
Fourth Order ◽  
Diclofenac Sodium ◽  
Environmental Water

Order determination of MA models using third- and fourth-order statistics

1998 ◽  
Vol 65 (3) ◽  
pp. 403-406 ◽  
Author(s):  
Diego P Ruiz ◽  
Antolino Gallego ◽  
Marı́a C Carrión ◽  
Jorge Portı́
Keyword(s):  
Order Statistics ◽  
Fourth Order ◽  
Order Determination

Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2013 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is required and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The equations presented, represent a complete set of Ri/t, a/t, and a/l ratios and include those presented in the 2012 PVP paper [8]. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. The equations developed in this paper will be added to the Appendix A procedures in the next major revision to ASME Section XI. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful when performing flaw growth evaluations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

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