TY - JOUR

T1 - “Wandering” eigenfrequencies of a two-dimensional elastic body with a blunted cusp

AU - Nazarov, S. A.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation, project no. 17-11-01003. Publisher Copyright: © 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85037164948&partnerID=8YFLogxK

U2 - 10.1134/S1028335817110040

DO - 10.1134/S1028335817110040

M3 - Article

AN - SCOPUS:85037164948

VL - 62

SP - 512

EP - 516

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 11

ER -