Force appropriation of nonlinear structures

TL;DR

This paper investigates the limitations of using phase quadrature conditions to identify nonlinear normal modes in structures, highlighting inaccuracies when limited excitation is applied and proposing energy transfer analysis for better understanding.

Contribution

It reveals the inaccuracies of the phase quadrature method under limited excitation and introduces energy transfer analysis to improve NNM identification in nonlinear structures.

Findings

Quadrature condition can significantly differ from true NNMs with limited excitation.

Energy transfer analysis helps identify regions of quadrature accuracy.

Multiple input forces improve NNM approximation accuracy.

Abstract

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly-used quadrature condition can give results that are significantly different from the true NNM, in particular when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped-clamped cross beam with two closely-spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.