2008
DOI: 10.1016/j.ijnonlinmec.2007.10.007
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Control of the homoclinic bifurcation in buckled beams: Infinite dimensional vs reduced order modeling

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Cited by 18 publications
(6 citation statements)
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“…For fixed-fixed b.c. and for a given value of Γ close to Γ cr,1 , this has been done in [30]. The results of the present work strongly call for a generalization m a n u s c r i p t of the homoclinic bifurcation analysis to other values of the axial parameter and to different b.c.…”
Section: Conclusion and Further Developmentssupporting
confidence: 56%
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“…For fixed-fixed b.c. and for a given value of Γ close to Γ cr,1 , this has been done in [30]. The results of the present work strongly call for a generalization m a n u s c r i p t of the homoclinic bifurcation analysis to other values of the axial parameter and to different b.c.…”
Section: Conclusion and Further Developmentssupporting
confidence: 56%
“…It corresponds to the governing equation obtained by the classical (linear) Galerkin projection of the dynamics onto the first linear mode. In fact, it is easy to verify that if we assume w(z,t)=x(t)w 1 (z), insert this expression in (1), multiply by w 1 (z) and integrate from z=0 to z=1, we get (30). It is worth to remark that (30) provides an exact result for the first family of b.c., for which α i =0, i=6,8,…, whereas just an unrefined approximation for the second family.…”
Section: Unrefined Rommentioning
confidence: 89%
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“…However, the matter of control can still be pursued, as already done -based on a refined theoretical treatment of the homoclinic bifurcation -in the limit case of a continuous (i.e., infinite d.o.f.) system, for the specific case of a buckled beam (Lenci and Rega, 2007). The results of this work call for an extension to more general situations.…”
Section: Conclusion and Further Developmentsmentioning
confidence: 82%
“…Some occurrences of homoclinic solutions can be regarded as the criterion from single well chaos to cross well chaos motion of oscillators [4], or as the onsets of chaotic vibrations of asymmetric nonconservative oscillators [5]. Homoclinic solutions were also adopted in bifurcation and chaotic vibration controls for beam structures [6,7]. Another typical application of homoclinic solutions aims at solitary wave studies.…”
Section: Introductionmentioning
confidence: 99%