| Title:
|
On Ishlinskij's model for non-perfectly elastic bodies (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1988 |
| Pages:
|
133-144 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator $F$, which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation $u'' + F(u)=0$ describing the motion of a mass point at the extremity of an elastico-plastic spring. (English) |
| Keyword:
|
damped vibrations |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
oscillatory properties |
| Keyword:
|
hysteresis scheme |
| Keyword:
|
Ishlinskij operator |
| Keyword:
|
potential energies |
| Keyword:
|
energy inequalities |
| Keyword:
|
dynamic behavior |
| Keyword:
|
non-perfect elasticity |
| MSC:
|
34A10 |
| MSC:
|
34G20 |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
34K99 |
| MSC:
|
46E35 |
| MSC:
|
47H99 |
| MSC:
|
73C50 |
| MSC:
|
73E99 |
| MSC:
|
74B99 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0653.73013 |
| idMR:
|
MR0940712 |
| DOI:
|
10.21136/AM.1988.104294 |
| . |
| Date available:
|
2008-05-20T18:34:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104294 |
| . |
| Reference:
|
[1] А.Ю. Ишлинский: Некоторые применения статистики к описанию законов деформирования тел.Изв. АН СССР, OTH, 1944, № 9, 583-590. Zbl 0149.19102 |
| Reference:
|
[2] M. А. Красносельский А. В. Покровский: Системы с гистерезисом.Москва, Наука, 1983. Zbl 1229.47001 |
| Reference:
|
[3] P. Krejčí: Hysteresis and periodic solutions of semilinear and quasilinear wave equations.Math. Z. 193 (1986), 247-264. MR 0856153, 10.1007/BF01174335 |
| Reference:
|
[4] P. Krejčí: Existence and large time behaviour of solutions to equations with hysteresis.Matematický ústav ČSAV, Praha, Preprint no. 21, 1986. |
| . |
