The subject of this paper is the multiple-time-scale analysis of Hopf bifurcations up to fifth-order nonlinearities. It is shown how an asymptotic fifth-order expansion captures the change in the nature of the limit cycle from stable to unstable and viceversa. The formulation is validated by applying it to a simple mechanical system for which there exists an analytical limit-cycle solution. Applications include the pre- and post-flutter behavior of a typical section with nonlinear spring having a stable limit cycle (supercritical Hopf bifurcation) that turns into an unstable one, because of fifth-order nonlinearities. (C) 2004 Elsevier Ltd. All rights reserved.
A fifth-order multiple-scale solution for Hopf bifurcations / Dessi, Daniele; Morino, Luigi; Mastroddi, Franco. - In: COMPUTERS & STRUCTURES. - ISSN 0045-7949. - STAMPA. - 82:31-32(2004), pp. 2723-2731. (Intervento presentato al convegno 2nd MIT Conference on Computational Fluid and Solid Mechanics tenutosi a CAMBRIDGE, MA nel JUN 17-20, 2003) [10.1016/j.compstruc.2004.07.009].
A fifth-order multiple-scale solution for Hopf bifurcations
DESSI, DANIELE;MORINO, Luigi;MASTRODDI, Franco
2004
Abstract
The subject of this paper is the multiple-time-scale analysis of Hopf bifurcations up to fifth-order nonlinearities. It is shown how an asymptotic fifth-order expansion captures the change in the nature of the limit cycle from stable to unstable and viceversa. The formulation is validated by applying it to a simple mechanical system for which there exists an analytical limit-cycle solution. Applications include the pre- and post-flutter behavior of a typical section with nonlinear spring having a stable limit cycle (supercritical Hopf bifurcation) that turns into an unstable one, because of fifth-order nonlinearities. (C) 2004 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
