Geodesic
Forced periodic vibrations of an elastic system with elastico-plastic damping
Applications of Mathematics, Tome 33 (1988) no. 2, pp. 145-153.

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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.
DOI : 10.21136/AM.1988.104295
Classification : 35B10, 35L70, 73D35, 73E50, 74H45, 74H99
Keywords: wave equation; hysteresis; Hooke law; elasto-plastic materials; existence; uniqueness; weak omega-periodic solutions; Ishlinskij operator 
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     author = {Krej\v{c}{\'\i}, Pavel},
     title = {Forced periodic vibrations of an elastic system with elastico-plastic damping},
     journal = {Applications of Mathematics},
     pages = {145--153},
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Krejčí, Pavel. Forced periodic vibrations of an elastic system with elastico-plastic damping. Applications of Mathematics, Tome 33 (1988) no. 2, pp. 145-153. doi : 10.21136/AM.1988.104295. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104295/

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