Asymptotic Behavior of an Unforced Duhem-Type Hysteretic Oscillator

TL;DR

This paper analyzes the fundamental analytical properties of an unforced Duhem-type hysteretic oscillator, establishing key results such as solution existence, uniqueness, and convergence to equilibrium.

Contribution

It provides new theoretical insights into the global behavior and stability of Duhem-type hysteretic oscillators in mechanical systems.

Findings

Proves global existence of solutions

Establishes uniqueness of solutions

Shows convergence to equilibrium

Abstract

The article describes fundamental analytical properties of an unforced mechanical oscillator with a Duhem-type viscoelastoplastic hysteretic element. These properties include global existence of solutions, uniqueness of solutions, and convergence of each solution to an equilibrium point.