 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 54, Issue 5 / 2019 | Next article >> |
| S.A. Nazarov, "Strange Behavior of Natural Oscillations of an Elastic Body with a Blunted Peak," Mech. Solids. 54 (5), 694-708 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
694-708 |
| DOI |
10.3103/S0025654419050121 |
| Title |
Strange Behavior of Natural Oscillations of an Elastic Body with a Blunted Peak |
| Author(s) |
S.A. Nazarov (St. Petersburg University, St. Petersburg, Russia; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia, srgnazarov@yahoo.co.uk) |
| Abstract |
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. |
| Keywords |
blunted peak, discrete and continuous spectrum, asymptotics, "blinking and gliding" eigenfrequencies |
| Received |
24 August 2018 | Revised |
25 December 2018 | Accepted |
04 January 2019 |
| Link to Fulltext |
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