SOLITON-LIKE OSCILLATIONS OF AN INFINITE BEAM ON A NONLINEARLY ELASTIC SUPPORT

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.