TY - JOUR

T1 - Strange Behavior of Natural Oscillations of an Elastic Body with a Blunted Peak

AU - Nazarov, S. A.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - The point of a peak on the surface of an elastic body Ω generates a continuous spectrum inducing wave processes in a finite volume (“black holes” for elastic waves). The spectrum of a body Ωh with a blunted peak is discrete, but the normal eigenvalues take on “strange behavior” as the length h of the broken tip tends to zero. In different situations, eigenvalues are revealed that do not leave the small neighborhood of the fixed point or, conversely, fall off along the real axis with high velocity, but smoothly decrease to the lower limit of the continuous spectrum of the body Ω. The chaotic wandering of eigenvalues above the second limit may occur. A new way of forming the continuous spectrum of the body Ω with a peak from the family of discrete spectra of the bodies Ωh with a blunted peak, h > 0, has been discovered.

AB - The point of a peak on the surface of an elastic body Ω generates a continuous spectrum inducing wave processes in a finite volume (“black holes” for elastic waves). The spectrum of a body Ωh with a blunted peak is discrete, but the normal eigenvalues take on “strange behavior” as the length h of the broken tip tends to zero. In different situations, eigenvalues are revealed that do not leave the small neighborhood of the fixed point or, conversely, fall off along the real axis with high velocity, but smoothly decrease to the lower limit of the continuous spectrum of the body Ω. The chaotic wandering of eigenvalues above the second limit may occur. A new way of forming the continuous spectrum of the body Ω with a peak from the family of discrete spectra of the bodies Ωh with a blunted peak, h > 0, has been discovered.

KW - asymptotics

KW - blunted peak

KW - discrete and continuous spectrum

KW - “blinking and gliding” eigenfrequencies

UR - http://www.scopus.com/inward/record.url?scp=85078957721&partnerID=8YFLogxK

U2 - 10.3103/S0025654419050121

DO - 10.3103/S0025654419050121

M3 - Article

AN - SCOPUS:85078957721

VL - 54

SP - 694

EP - 708

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 5

ER -