Imperial College London

DrLoicSalles

Faculty of EngineeringDepartment of Mechanical Engineering

Research Fellow
 
 
 
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Contact

 

+44 (0)20 7594 2243l.salles Website

 
 
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Assistant

 

Mr Peter Higgs +44 (0)20 7594 7078

 
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Location

 

556City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Vizzaccaro:2020,
author = {Vizzaccaro, A and Salles, L and Touzé, C},
journal = {Nonlinear Dynamics},
title = {Comparison of nonlinear mappings for reduced-order modellingof vibrating structures: normal form theory and quadraticmanifold method with modal derivatives},
url = {http://hdl.handle.net/10044/1/81347},
year = {2020}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to obtain a nonlinear change of coordinates for expressing the reduced-order dynamics in an invariant-based span of the phase space. The second method is the modal derivative (MD) approach, and more specifically the quadratic manifold defined in order to derive a second-order nonlinear change of coordinates. Both methods share a common point of view, willing to introduce a nonlinear mapping to better define a reduced-order model that could take more properly into account the nonlinear restoring forces. However the calculation methods are different and the quadratic manifold approach has not the in variance property embedded in its definition. Modal derivatives and static modal derivatives are investigated, and their distinctive features in the treatment of the quadratic nonlinearity is underlined.Assuming a slow/fast decomposition allows understanding how the three methods tend to share equivalent properties. While they give proper estimations for flat symmetric structures having a specific shape of nonlinearities and a clear slow/fast decomposition between flexural and in-plane modes, the treatment of the quadratic nonlinearity makes the predictions different in the case of curved structures such as arches and shells. In the more general case, normal form approach appears preferable since it allows correct predictions of a number of important nonlinear features,including for example the hardening/softening behaviour, whatever the relationships between slave and master coordinates are.
AU - Vizzaccaro,A
AU - Salles,L
AU - Touzé,C
PY - 2020///
SN - 0924-090X
TI - Comparison of nonlinear mappings for reduced-order modellingof vibrating structures: normal form theory and quadraticmanifold method with modal derivatives
T2 - Nonlinear Dynamics
UR - http://hdl.handle.net/10044/1/81347
ER -