Application of control-based continuation to a nonlinear structure with harmonically coupled modes

TL;DR

This paper demonstrates how control-based continuation (CBC) can be systematically applied to multi-degree-of-freedom nonlinear structures to extract complex dynamical features directly from experiments without relying on models.

Contribution

It extends CBC methodology from single-DOF to multi-DOF systems, enabling direct experimental exploration of nonlinear dynamics in complex structures.

Findings

CBC successfully extracted nonlinear features like an isola from experiments.

The method was validated against open-loop measurements with good agreement.

Careful handling of higher-harmonics is necessary for accurate force application.

Abstract

This paper presents a systematic method for exploring the nonlinear dynamics of multi-degree-of-freedom (MDOF) physical experiments. To illustrate the power of this method, known as control-based continuation (CBC), it is applied to a nonlinear beam structure that exhibits a strong 3:1 modal coupling between its first two bending modes. CBC is able to extract a range of dynamical features, including an isola, directly from the experiment without recourse to model fitting or other indirect data-processing methods. Previously, CBC has only been applied to (essentially) single-degree-of-freedom experiments; in this paper we show that the required feedback-control methods and path-following techniques can equally be applied to MDOF systems. A low-level broadband excitation is initially applied to the experiment to obtain the requisite information for controller design and, subsequently, the physical experiment is treated as a `black box' that is probed using CBC. The invasiveness of the controller used is analysed and experimental results are validated with open-loop measurements. Good agreement between open- and closed-loop results is achieved, though it is found that care needs to be taken in dealing with the presence of higher-harmonics in the force applied to the structure.