MEMBRANE DEFORMATION BY A MOVING LOAD

Small steady deformations (displacements) of the elements of a homogen eous membrane caused by a [force] load moving uniformly along one of t he axes with velocity exceeding the velocity of propagation of elastic waves in the membrane are investigated The cases of a toad distribute d along the other axis and concentrated loads are considered. Deformat ions for an unbounded membrane, a half-plane and an unbounded strip ar e analysed. A method is used which enables a new independent variable to be introduced and enables a problem equivalent to the action of a m oving load or a system of moving loads on an unbounded or half-bounded string to be obtained. Problems with central symmetry are also consid ered. Namely, it is assumed that an undeformable disc is attached rigi dly to an unbounded membrane and a concentrated [force] load is moving at constant velocity around a circle with the same centre as the disk . An investigation of the problem in polar coordinates enables it to b e reduced to the general form of the problem of the deformation of a s tring. By applying the appropriate results obtained earlier for a stri ng [1] the following qualitative result is established: there are valu es of the velocity of motion of the load such that no work is performe d in overcoming wave resistance forces in the steady state, which is e quivalent to the absence of such forces. (C) 1997 Elsevier Science Ltd . All rights reserved.