Forced nonlinear oscillations of semi-infinite cables and beams resting on a unilateral elastic substrate
NONLINEAR DYNAMICS
Autore/i: Demeio, Lucio; Lenci, Stefano
Editore: Kluwer Academic Publishers:Journals Department, PO Box 322, 3300 AH Dordrecht Netherlands:011 31 78 6576050, EMAIL: frontoffice@wkap.nl, kluweronline@wkap.nl, INTERNET: http://www.kluwerlaw.com, Fax: 011 31 78 6576254
Classificazione: 1 Contributo su Rivista
Abstract: In this work, we study the nonlinear oscillations
of mechanical systems resting on a (unilateral)
elastic substrate reacting in compression only.We consider
both semi-infinite cables and semi-infinite beams,
subject to a constant distributed load and to a harmonic
displacement applied to the finite boundary. Due to the
nonlinearity of the substrate, the problem falls in the
realm of free-boundary problems, because the position
of the points where the system detaches from the substrate,
called Touch Down Points (TDP), is not known
in advance. By an appropriate change of variables, the
problem is transformed into a fixed-boundary problem,
which is successively approached by a perturbative expansion
method. In order to detect the main mechanical
phenomenon, terms up to the second order have to be
considered. Two different regimes have been identified
in the behaviour of the system, one below (called subcritical)
and one above (called supercritical) a certain
critical excitation frequency. In the latter, energy is lost
by radiation at infinity, while in the former this phenomenon
does not occur and various resonances are observed instead; their number depends on the statical
configuration around which the system performs nonlinear
oscillations.
Scheda della pubblicazione: https://iris.univpm.it/handle/11566/31375