Thermoelastoplastic oscillator with Prandtl-Ishlinskii operator

We study a mathematical model of mass points longitudinally oscillating between thermoelastoplastic springs. It is derived as a discrete version of a continuous model of longitudinal oscillations of a one-dimensional object. The problem is formulated as a system of nonlinear ordinary differential equations with Prandtl-Ishlinskii type of nonlinearity, subsequently simplified using the first integral of the energy. We show that the system is asymptotically directed to one of the many possible steady states, where all movements cease and temperatures equalize.