Article
MSC:
34A10,
34G20,
34K15,
34K25,
34K99,
46E35,
47H99,
73C50,
73E99,
74B99,
74S30 | MR 0940712 | Zbl 0653.73013 | DOI: 10.21136/AM.1988.104294
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Keywords:
damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity
damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity
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.
References:
[1] А.Ю. Ишлинский: Некоторые применения статистики к описанию законов деформирования тел. Изв. АН СССР, OTH, 1944, № 9, 583-590. Zbl 0149.19102
[2] M. А. Красносельский А. В. Покровский: Системы с гистерезисом. Москва, Наука, 1983. Zbl 1229.47001
[3] P. Krejčí: Hysteresis and periodic solutions of semilinear and quasilinear wave equations. Math. Z. 193 (1986), 247-264. DOI 10.1007/BF01174335 | MR 0856153
[4] P. Krejčí: Existence and large time behaviour of solutions to equations with hysteresis. Matematický ústav ČSAV, Praha, Preprint no. 21, 1986.
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