On second-order anharmonic constants forXY 2 molecules in the local-mode approach

1999 ◽  
Vol 42 (5) ◽  
pp. 457-461 ◽  
Author(s):  
O. N. Ulenikov ◽  
S. N. Yurchenko
Keyword(s):  
Second Order ◽  
Local Mode ◽  
Anharmonic Constants

Imperfection Sensitivity of Stiffened Cylindrical Shells Under Interactive Buckling

1994 ◽  
Vol 47 (6S) ◽  
pp. S251-S255
Author(s):  
Srinivasan Sridharan
Keyword(s):  
Amplitude Modulation ◽  
Cylindrical Shells ◽  
Computational Modelling ◽  
Local Buckling ◽  
Second Order ◽  
New Technique ◽  
Local Mode ◽  
Imperfection Sensitivity ◽  
Stiffened Shells ◽  
Stiffened Cylindrical Shells

In this paper some recent advances made in the understanding of the phenomena and computational modelling of the interaction of local and overall instabilities in stiffened cylindrical shells will be reviewed. These relate to two distinct categories of problems: (1) Axially compressed stringer-stiffened shells and (2) Ring-stiffened cylinders subjected to hydrostatic compression. The former have been analyzed with a novel methodology which employs finite elements in which the local buckling information is embedded. Comparisons of the results of the new technique with Abaqus - a well established nonlinear analysis program - reveals the validity of the underlying concepts of the new technique and efficacy of the new approach. It is shown, that provided all the key local buckling modes triggered in the interaction are considered and the modulation of local buckling amplitudes is accounted for, it is justifiable to neglect the mixed second order stresses and strains in the analysis. Imperfection-sensitivity of a stringer stiffened cylindrical shell structure is illustrated. In the case ring-stiffened cylinders subjected to hydrostatic pressure, it is shown that the amplitude modulation is the key factor in the interaction; it performs the function of capturing the contributions of several neighboring modes of the same longitudinal description as the fundamental local mode, but with differing circumferential wave numbers. An examination of the potential energy function indicates that the amplitude modulation is solely responsible for the presence of the nonvanishing cubic terms, which are dominant over the quartic terms. Once again, mixed second order fields evaluated with appropriate orthogonality conditions have little influence on the interaction and can be safely neglected. An example of an orthotropic layered shell under coincident and well separated critical stresses is presented.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Subsystems of Second Order Arithmetic

2009 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic

Anharmonically-coupled local mode to normal mode Hamiltonian transformations: beyond the x, K-relations

1998 ◽  
Vol 93 (5) ◽  
pp. 821-830
Author(s):  
M.M. LAW ◽  
J.L. DUNCAN
Keyword(s):  
Normal Mode ◽  
Local Mode

Second order interference in two photon absorption

1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT
Keyword(s):  
Second Order ◽  
Photon Absorption ◽  
Two Photon Absorption ◽  
Two Photon
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