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damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity
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.
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