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The landscape of nonlinear structural dynamics: an introduction
T Butlin1, J Woodhouse2, A R Champneys3
1Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK tb267@cam.ac.uk.
Summary
Nonlinear behavior in engineering structures, including amplitude-dependent frequencies and self-excited oscillations, is common. This work introduces a mind-map to guide practitioners in analyzing and controlling these complex nonlinear phenomena.
Area of Science:
- Mechanical Engineering
- Applied Mathematics
- Vibrational Dynamics
Background:
- Nonlinear behavior is a pervasive characteristic of vibrating engineering structures.
- Common manifestations include amplitude-dependent natural frequencies, buzz, squeak, rattle, self-excited oscillations, and non-repeatability.
Purpose of the Study:
- To provide an extended introduction to nonlinear phenomena in engineering vibrations.
- To offer a structured guide for identifying, analyzing, controlling, and exploiting nonlinear behaviors.
- To contextualize the engineering applications and mathematical techniques for nonlinear dynamics.
Main Methods:
- Expert elicitation was used to create a mind-map of the nonlinear dynamics landscape.
- The mind-map organizes engineering contexts and mathematical techniques.
- A software implementation of the mind-map is available as electronic supplementary material.
Main Results:
- A comprehensive mind-map illustrating the field of nonlinear dynamics in engineering.
- Diverse case studies are presented to highlight various nonlinear phenomena.
- The mind-map serves as a practitioner's guide to a complex research area.
Conclusions:
- Nonlinear behavior in engineering structures is a significant area of study.
- The developed mind-map provides a structured approach to understanding and managing nonlinear dynamics.
- This resource aims to demystify the complex landscape of nonlinear vibration analysis and control.
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