Extension of the single-nonlinear-mode theory by linear attachments and application to exciter-structure interaction

TL;DR

This paper extends the single-nonlinear-mode theory to include linear attachments of various physical types, enabling simplified analysis of complex coupled systems like exciter-structure interactions with diverse applications.

Contribution

It introduces a theoretical extension allowing linear attachments to be modeled with a single nonlinear mode, broadening the applicability beyond purely mechanical systems.

Findings

The extended theory accurately models exciter-structure interaction.

Linear attachments can be represented by modal impedance and forcing.

The approach simplifies analysis of coupled systems with diverse physical models.

Abstract

Under certain conditions, the dynamics of a nonlinear mechanical system can be represented by a single nonlinear modal oscillator. The properties of the modal oscillator can be determined by computational or experimental nonlinear modal analysis. The simplification to a single-nonlinear-mode model facilitates qualitative and global analysis, and substantially reduces the computational effort required for probabilistic methods and design optimization. Important limitations of this theory are that only purely mechanical systems can be analyzed and that the respective nonlinear mode has to be recomputed when the system's structural properties are varied. With the theoretical extension proposed in this work, it becomes feasible to attach linear subsystems to the primary mechanical system, and to approximate the dynamics of this coupled system using only the nonlinear mode of the primary mechanical system. The attachments must be described by linear ordinary or differential-algebraic equations with time-invariant coefficient matrices. The attachments do not need to be of purely mechanical nature, but may contain, for instance, electric, magnetic, acoustic, thermal or aerodynamic models. This considerably extends the range of utility of nonlinear modes to applications as diverse as model updating or vibration energy harvesting. As long as the attachments do not significantly deteriorate the host system's modal deflection shape, it is shown that their effect can be reduced to a complex-valued modal impedance and an imposed modal forcing term. In the present work, the proposed approach is computationally assessed for the analysis of exciter-structure interaction. More specifically, the force drop typically encountered in frequency response testing is revisited.