@article{Sarrouy_2011a,
title = {Global and bifurcation analysis of a structure with cyclic symmetry},
author = { Emmanuelle Sarrouy and Aur\'{e}lien Grolet and Fabrice Thouverez},
doi = {10.1016/j.ijnonlinmec.2011.02.005},
year = {2011},
date = {2011-01-01},
journal = {International Journal of Non-Linear Mechanics},
volume = {46},
pages = {727--737},
keywords = {Bifurcation, Continuation, Global analysis, Nonlinear Normal Modes (NNM)},
pubstate = {published},
tppubtype = {article}
}
@article{Sarrouy_2010,
title = {Global search of non-linear systems periodic solutions: A rotordynamics application},
author = { Emmanuelle Sarrouy and Fabrice Thouverez},
url = {http://www.sciencedirect.com/science/article/B6WN1-4YC1K3B-2/2/7abae13482c7f6495651c5642074be84},
doi = {DOI: 10.1016/j.ymssp.2010.02.001},
issn = {0888-3270},
year = {2010},
date = {2010-01-01},
journal = {Mechanical Systems and Signal Processing},
volume = {24},
number = {6},
pages = {1799-1813},
abstract = {Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.},
keywords = {Global analysis},
pubstate = {published},
tppubtype = {article}
}
Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.