Abstract
Small steady deformations (displacements) of the elements of a homogeneous membrane caused by a [force] load moving uniformly along one of the axes with velocity exceeding the velocity of propagation of elastic waves in the membrane are investigated. The cases of a load distributed along the other axis and concentrated loads are considered. Deformations for an unbounded membrane, a half-plane and an unbounded strip are analysed. A method is used which enables a new independent variable to be introduced and enables a problem equivalent to the action of a moving load or a system of moving loads on an unbounded or half-bounded string to be obtained. Problems with central symmetry are also considered. Namely, it is assumed that an undeformable disc is attached rigidly 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 be reduced to the general form of the problem of the deformation of a string. By applying the appropriate results obtained earlier for a string [1] the following qualitative result is established: there are values of the velocity of motion of the load such that no work is performed in overcoming wave resistance forces in the steady state, which is equivalent to the absence of such forces.
Published Version
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