Phase resonance nonlinear modes of mechanical systems

TL;DR

This paper introduces a computational framework to predict phase resonance nonlinear modes in mechanical systems, accurately capturing various resonance types and phase lags beyond traditional pi/2 assumptions.

Contribution

It develops a novel method to identify phase resonance nonlinear modes, including superharmonic, subharmonic, and ultra-subharmonic resonances, in nonlinear mechanical systems.

Findings

Framework accurately predicts phase resonance modes.

Captures superharmonic, subharmonic, ultra-subharmonic resonances.

Demonstrated on systems with cubic nonlinearity.

Abstract

The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase resonance of nonlinear mechanical systems subjected to single-point, single-harmonic excitation. In this context, the main contribution of this paper is to develop a computational framework which can predict the mode shapes and oscillation frequencies at phase resonance. The resulting nonlinear modes are termed phase resonance nonlinear modes (PRNMs). A key property of PRNMs is that, besides primary resonances, they can accurately characterize superharmonic, subharmonic and ultra-subharmonic resonances for which, as shall be shown in this paper, phase lags at resonance may be different from pi/2. The proposed developments are demonstrated using one- and two-degree-of-freedom systems featuring a cubic nonlinearity.