| Title:
|
Forced periodic vibrations of an elastic system with elastico-plastic damping (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1988 |
| Pages:
|
145-153 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations $u_{tt} - \Delta_xu \pm F(u) = g(x,t)$ for an arbitrary (sufficiently smooth) periodic right-hand side $g$, where $\Delta_x$ denotes the Laplace operator with respect to $x\in \Omega \subset R^N, N\geq 1$, and $F$ is the Ishlinskii hysteresis operator. For $N=2$ this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium. (English) |
| Keyword:
|
wave equation |
| Keyword:
|
hysteresis |
| Keyword:
|
Hooke law |
| Keyword:
|
elasto-plastic materials |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
weak omega-periodic solutions |
| Keyword:
|
Ishlinskij operator |
| MSC:
|
35B10 |
| MSC:
|
35L70 |
| MSC:
|
73D35 |
| MSC:
|
73E50 |
| MSC:
|
74H45 |
| MSC:
|
74H99 |
| idZBL:
|
Zbl 0649.73029 |
| idMR:
|
MR0940713 |
| DOI:
|
10.21136/AM.1988.104295 |
| . |
| Date available:
|
2008-05-20T18:34:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104295 |
| . |
| Reference:
|
[1] О. В. Бесов В. П. Ильин С. М. Никольский: Интегральные представления функций и теоремы вложения.Москва, Наука, 1975. Zbl 1231.90252 |
| Reference:
|
[2] A. IO. Ишлинский: Некоторые применения статистики к описанию законов деформирования тел.Изв. АН СССР, OTH, 1944, но. 9, 583-590. Zbl 0149.19102 |
| Reference:
|
[3] M. А. Красносельский А. В. Покровский: Системы с гистерезисом.Москва, Наука, 1983. Zbl 1229.47001 |
| Reference:
|
[4] P. Krejčí: Hysteresis and periodic solutions of semilinear and quasilinear wave equations.Math. Z. 193 (1986), 247-264. MR 0856153, 10.1007/BF01174335 |
| Reference:
|
[5] P. Krejčí: On Ishlinskii's model for non-perfectly elastic bodies.To appear. |
| Reference:
|
[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[7] A. Visintin: On the Preisach model for hysteresis.Nonlinear Anal. T.M.A. 8 (1984), 977-996. Zbl 0563.35007, MR 0760191 |
| Reference:
|
[8] A. Visintin: Evolution problems with hysteresis in the source term.Ist. Anal. Num. C.N.R., Pavia, Italy. Preprint no. 326. Zbl 0618.35053, MR 0853520 |
| . |
