“Wandering” eigenfrequencies of a two-dimensional elastic body with a blunted cusp

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Abstract

At the pointed cusp of a two-dimensional plate, a tip of small length h is broken off. By means of asymptotic analysis, a new effect of “wandering” of eigenfrequencies of longitudinal vibrations of the plate with the blunted cusp is found: as h → +0, the frequencies prove to be almost periodic functions in the logarithmic scale ln h; i.e., when the fragment length decreases, they chaotically move at a high speed O(h−1) along the real semi-axis (κ, +∞), while κ > 0 is the cutoff point of the continuous spectrum of the problem with an ideal cusp.

Original languageEnglish
Pages (from-to)512-516
Number of pages5
JournalDoklady Physics
Volume62
Issue number11
DOIs
StatePublished - 1 Nov 2017

Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)

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