Forced periodic vibrations of an elastic system with elastico-plastic damping
Aplikace matematiky (1988)
- Volume: 33, Issue: 2, page 145-153
- ISSN: 0862-7940
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topKrejčí, Pavel. "Forced periodic vibrations of an elastic system with elastico-plastic damping." Aplikace matematiky 33.2 (1988): 145-153. <http://eudml.org/doc/15531>.
@article{Krejčí1988,
abstract = {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 $x\in \Omega \subset R^N, N\ge 1$, 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.},
author = {Krejčí, Pavel},
journal = {Aplikace matematiky},
keywords = {wave equation; hysteresis; Hooke law; elasto-plastic materials; existence; uniqueness; weak omega-periodic solutions; Ishlinskij operator; wave equation; hysteresis; Hooke law; elasto-plastic materials; existence; uniqueness; weak omega-periodic solutions; Ishlinskij operator},
language = {eng},
number = {2},
pages = {145-153},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Forced periodic vibrations of an elastic system with elastico-plastic damping},
url = {http://eudml.org/doc/15531},
volume = {33},
year = {1988},
}
TY - JOUR
AU - Krejčí, Pavel
TI - Forced periodic vibrations of an elastic system with elastico-plastic damping
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 2
SP - 145
EP - 153
AB - 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 $x\in \Omega \subset R^N, N\ge 1$, 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.
LA - eng
KW - wave equation; hysteresis; Hooke law; elasto-plastic materials; existence; uniqueness; weak omega-periodic solutions; Ishlinskij operator; wave equation; hysteresis; Hooke law; elasto-plastic materials; existence; uniqueness; weak omega-periodic solutions; Ishlinskij operator
UR - http://eudml.org/doc/15531
ER -
References
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- P. Krejčí, 10.1007/BF01174335, Math. Z. 193 (1986), 247-264. (193) MR0856153DOI10.1007/BF01174335
- P. Krejčí, On Ishlinskii's model for non-perfectly elastic bodies, To appear.
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