Identifying the significance of nonlinear normal modes

Tom Hill; Andrea Cammarano; Simon Neild; David Barton

doi:10.1098/rspa.2016.0789

Identifying the significance of nonlinear normal modes

Tom Hill, Andrea Cammarano, Simon Neild, David Barton

Research output: Contribution to journal › Article (Academic Journal) › peer-review

34 Citations (Scopus)

341 Downloads (Pure)

Abstract

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system - highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared to simulated forced responses to verify these findings.

Original language	English
Article number	20160789
Number of pages	25
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	473
Early online date	1 Mar 2017
DOIs	https://doi.org/10.1098/rspa.2016.0789
Publication status	Published - Mar 2017

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

structural dynamics
nonlinear normal modes
backbone curves
energy transfer
resonance
second-order normal form technique

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10.1098/rspa.2016.0789

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This is the final published version of the article (version of record). It first appeared online via the Royal Society at http://rspa.royalsocietypublishing.org/content/473/2199/20160789. Please refer to any applicable terms of use of the publisher.
Final published version, 1.5 MBLicence: CC BY

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Dynamic design tools for understanding and exploiting nonlinearity in structures
Neild, S. A. (Principal Investigator)
1/02/13 → 31/07/18
Project: Research

indentifying significance of nnms
Neild, S. (Creator) & Hill, T. (Creator), University of Bristol, 20 Jan 2017
DOI: 10.5523/bris.18ov1ijiiox0u1b0z40rzcsnwl, http://data.bris.ac.uk/data/dataset/18ov1ijiiox0u1b0z40rzcsnwl
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Dr Tom L Hill
- tom.hillbristol.acuk
- School of Electrical, Electronic and Mechanical Engineering - Lecturer
- Dynamics and Control
Person: Academic , Member

Cite this

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title = "Identifying the significance of nonlinear normal modes",

abstract = "Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system - highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared to simulated forced responses to verify these findings.",

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year = "2017",

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language = "English",

volume = "473",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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T1 - Identifying the significance of nonlinear normal modes

AU - Hill, Tom

AU - Cammarano, Andrea

AU - Neild, Simon

AU - Barton, David

PY - 2017/3

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N2 - Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system - highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared to simulated forced responses to verify these findings.

AB - Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system - highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared to simulated forced responses to verify these findings.

KW - structural dynamics

KW - nonlinear normal modes

KW - backbone curves

KW - energy transfer

KW - resonance

KW - second-order normal form technique

U2 - 10.1098/rspa.2016.0789

DO - 10.1098/rspa.2016.0789

M3 - Article (Academic Journal)

C2 - 28413342

SN - 1364-5021

VL - 473

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

M1 - 20160789

ER -

Identifying the significance of nonlinear normal modes

Abstract

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Dynamic design tools for understanding and exploiting nonlinearity in structures

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indentifying significance of nnms

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Dr Tom L Hill

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