THE DYNAMICAL ANALYSIS OF A FINITE INEXTENSIBLE BEAM WITH AN ATTACHEDACCELERATING MASS

The objective of this paper is an analytical and numerical study of th e dynamics of a beam with attached masses. Specifically, a finite inex tensible beam that rests on a uniform elastic foundation and carries a n accelerating mass is considered. Of interest is the dynamics of the beam-mass system due to the motion of the moving mass. The influence o f various parameters such as forward force, retard force and friction upon the performance of the beam are investigated. The mechanics of th e problem is Newtonian. Based on the assumption that when the moving m ass is set in motion the mass is assumed to be rolling on the beam, th e mechanics, including effects due to friction and convective accelera tions of the interface between the moving mass and the beam, are deter mined. The problem of the system is nonlinear, due to the presence of friction and the convective acceleration. In the modeling, the mass ca n be accelerated by a force. Meanwhile, the mass is capable of reducin g speed and-being brought to a stop at any position on the beam by app lying a retard force to the mass and/or increasing the friction betwee n the mass and the beam. The force is assumed to be tangential to the deformed configuration of the beam. By employing the Galerkin procedur e, the partial differential equations which describe the transient vib rations of the beam-mass system are reduced to an initial value proble m with finite dimensions. The method of numerical integration is used to get convergent solutions. (C) 1997 Elsevier Science Ltd.