Bs. Bardin et Sd. Furta, SOLITON-LIKE OSCILLATIONS OF AN INFINITE BEAM ON A NONLINEARLY ELASTIC SUPPORT, Chaos, solitons and fractals, 9(1-2), 1998, pp. 145-156
This article deals with travelling wave motions of a homogeneous infin
ite elastic beam. It is assumed that the beam lies on a dense support.
The authors describe that support as an infinite set of identical spr
ings obeying a non-linear deformation law. It has been proven that the
above motions can be described by means of a Hamiltonian system of eq
uations with two degrees of freedom. The authors use local methods of
Hamiltonian mechanics and some wall known results of the KAM-theory to
analytically investigate the system under consideration. The authors
give conditions to existence of solitary wave motions and derive their
asymptotic representations. To check the analytic results, the author
s fulfil certain numerical experiments. The above conditions to existe
nce are revised with the help of the Poincare map method. (C) 1998 Els
evier Science Ltd. All rights reserved.