caa a22 4500 469081562 CHVBK 20180323132951.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01170813 doi (NATIONALLICENCE)springer-10.1007/BF01170813 Vakakis A. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urabana, IL, USA aut Dynamics of a nonlinear periodic structure with cyclic symmetry [Elektronische Daten] [A. Vakakis] Summary: The free and forced motions of a nonlinear periodic structure with cyclic symmetry are studied. The structure consists of a number of identical linear flexural members coupled by means of nonlinear stiffnesses of the third degree. It is found that this system can only possessn "similar” nonlinear modes of free oscillation, and that no other modes are possible. Moreover, there exist pairs of nonlinear modes with mutually orthogonal nodal diameters having, in general, distinct "backbone” curves. A multiple-scales averaging analysis is used to study the nonlinear interaction between a pair of modes with orthogonal nodal diameters. As a result of this analysis, it is found that all pairs of nonliner modes along with all their linear combinations are orbitally unstable, and the only possible orbitally stable periodic motions are free travelling waves, that propagate through the structure in the clockwise and anti-clockwise directions. Under harmonic forcing, a bifuraction of a stable branch of forced travelling waves from a branch of forced normal mode motions is detected, and "jump” phenomena between branches of periodic solutions are observed. The analytical results are in agreement with experimental observations of an earlier work, and, in addition, are verified by numerical simulations. Springer-Verlag, 1992 Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 197-226 0001-5970 95:1-4<197 1992 95 707 https://doi.org/10.1007/BF01170813 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01170813 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vakakis A. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urabana, IL, USA aut NATIONALLICENCE 773 0- Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 197-226 0001-5970 95:1-4<197 1992 95 707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer