An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems

TL;DR

This paper introduces a computationally efficient frequency domain method for approximating resonance curves in weakly-damped nonlinear mechanical systems, focusing on steady-state vibrations and capable of revealing isolated solution branches.

Contribution

It presents a novel method that assumes constant phase lag to trace resonance peaks efficiently in weakly-damped nonlinear systems, validated on specific mechanical models.

Findings

Method offers superior computational efficiency.

Applicable to weakly-damped nonlinear systems.

Can reveal isolated solution branches.

Abstract

A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates in the frequency domain and its central idea is to assume a constant phase lag between forcing and response. The method is validated for a two-degree-of-freedom oscillator with cubic spring and a bladed disk with shroud contact. The method provides superior computational efficiency, but is limited to weakly-damped systems. Finally, the capability to reveal isolated solution branches is highlighted.