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Results for “Double Hopf singularity”

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2 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The infinite level normal forms for non-resonant double Hopf singularities

Here, in this paper, we explore hypernormal forms of vector fields that have non-resonant double Hopf singularities with a non-zero radial cubic part. Our primary focus is on investigating the infinite-level normal form classification of this type of singularities. We provide a normal form decomposition in terms of planar-rotating and planar-radial vector fields, which greatly facilitate the pattern recognition and analysis of the corresponding generalized homological maps. Notably, our paper represents the first instance of the normal form classification for general non-resonant double Hopf singularities without structural symmetry.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

The stress intensity factor for the double cantilever beam

Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the double cantilever beam (DCB) specimen. In place of the Dirac delta function, a family of functions which duplicates the important features of the concentrated forces without introducing unmanageable mathematical complexities is used as a loading function. With terms of order h-squared/a-squared retained in the series expansion, the dimensionless stress intensity factor is found to be K (h to the 1/2)/P = 12 to the 1/2 (a/h + 0.6728 + 0.0377 h-squared/a-squared), in which P is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, and h is the height of each cantilever beam. The result is similar to that obtained by Gross and Srawley by fitting a line to discrete results from their boundary collocation analysis.

Fichter, W. B.↗