caa a22 4500 445361182 CHVBK 20180317142915.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s11071-010-9787-2 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9787-2 Detecting stable-unstable nonlinear invariant manifold andhomoclinic orbits in mechanical systems [Elektronische Daten] [Stefano Lenci, Giuseppe Rega] We consider a four-dimensional Hamiltonian system representing the reduced-order (two-mode) dynamics of a buckled beam, where the nonlinearity comes from the axial deformation in moderate displacements, according to classical theories. The system has a saddle-center equilibrium point, and we pay attention to the existence and detection of the stable-unstable nonlinear manifold and of homoclinic solutions, which are the sources of complex and chaotic dynamics observed in the system response. The system has also a coupling nonlinear parameter, which depends on the boundary conditions, and is zero, e.g., for the beam hinged-hinged ends and different from zero, e.g., for the beam fixed-fixed ends. The invariant manifold in the latter case is detected assuming that it can be represented as a graph over the plane spanned by the unstable (principal) variable and its velocity. We show by a series solution that the manifold exists but has a limited extension, not sufficient for the deployment of the homoclinic orbit. Thus, the homoclinic orbit is addressed directly, irrespective of its belonging to the invariant manifold. By means of the perturbation method, it is shown that it exists only on some curves of the governing parameters space, which branch from a fundamental path. This shows that the homoclinic orbit is not generic. These results have been confirmed by numerical simulations and by a different analytical technique. Springer Science+Business Media B.V., 2010 Buckled beam nationallicence Saddle-center nationallicence Invariant manifold nationallicence Homoclinic orbits nationallicence Lenci Stefano Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131, Ancona, Italy aut Rega Giuseppe Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Roma, Italy aut Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 83-94 0924-090X 63:1-2<83 2011 63 11071 https://doi.org/10.1007/s11071-010-9787-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9787-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lenci Stefano Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131, Ancona, Italy aut NATIONALLICENCE 700 1- Rega Giuseppe Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, via A. Gramsci 53, 00197, Roma, Italy aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 83-94 0924-090X 63:1-2<83 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer