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

L. Renson, Alexander Shaw Orcid Logo, D.A.W. Barton, S.A. Neild

Mechanical Systems and Signal Processing, Volume: 120, Pages: 449 - 464

Swansea University Author: Alexander Shaw Orcid Logo

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 couplin...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa44937
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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 (SDOF) experiments. This is the first experimental demonstration of CBC in the presence of complex MDOF response features such as internal resonance, isola, and Neimark-Sacker bifurcations. In this paper we show that the feedback-control methods and path-following techniques used in a SDOF context 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.
Keywords: Nonlinear dynamics, Experiment, Control-based continuation, Multi-degree-of-freedom, Modal interaction, Isola
College: College of Engineering
Start Page: 449
End Page: 464