Nonlinear-damped Duffing oscillators having finite time dynamics

TL;DR

This paper introduces a class of nonlinear-damped Duffing oscillators that exhibit finite time dynamics, where oscillations cease after a finite number of cycles, relevant for modeling nano-structures and macroscopic beams.

Contribution

It presents a novel class of modified Duffing oscillators with nonlinear damping that have finite time oscillatory behavior, advancing understanding of damping effects in complex systems.

Findings

Solutions oscillate finitely before stopping

Applicable to nano-structure and macro-structure vibrations

Provides new insights into nonlinear damping effects

Abstract

A class of modified Duffing oscillator differential equations, having nonlinear damping forces, are shown to have finite time dynamics, i.e., the solutions oscillate with only a finite number of cycles, and, thereafter, the motion is zero. The relevance of this feature is briefly discussed in relationship to the mathematical modeling, analysis, and estimation of parameters for the vibrations of carbon nano-tubes and graphene sheets, and macroscopic beams and plates.