Nonlinear Generalization of Den Hartog's Equal-Peak Method

TL;DR

This paper introduces a nonlinear tuned vibration absorber (NLTVA) tailored to the primary system's nonlinear restoring force, using a generalized Den Hartog's equal-peak method to effectively mitigate nonlinear resonance in mechanical systems.

Contribution

It proposes a novel nonlinear vibration absorber design and a generalized method for parameter tuning based on the nonlinear restoring force of the primary system.

Findings

NLTVA effectively reduces nonlinear resonance vibrations.

The generalized tuning method extends classical approaches to nonlinear systems.

Application to Duffing oscillator demonstrates practical effectiveness.

Abstract

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.