The work of a source maintaining a uniform motion of a load along an elastically supported membrane

Analytical expressions for the transverse displacement of a membrane mounte d on an elastic base and subjected to a uniformly moving load are derived. Two cases are considered: a subcritical motion when the load velocity Vis l ess than the wave propagation velocity in the membrane c and a supercritica l motion when V > c. A general expression for the work provided by a source maintaining the uniform motion of a concentrated load along the membrane i s obtained. In the absence of the energy loss in the membrane, this work is equal to zero for the subcritical motion and tends to infinity for the sup ercritical motion. The tatter result is a consequence of the discontinuity of the solution obtained for the membrane displacement. With the introducti on of the internal friction in the membrane, it is possible to eliminate th is discontinuity. On the basis of the numerical solution to the problem wit h internal friction, the dependence of the work of the external source on t he load velocity is analyzed. (C) 2000 MAIK "Nauka/Interperiodica".