Radiation emitted by a constant load moving uniformly in a circle on an elastically supported membrane

Wave radiation is studied which is due a constant load moving with a constant speed along a circular path over an unbounded membrane on a elastic foundation. The steady-state solution of the problem is obtained, showing that the radiation occurs for all load velocities. It is shown that the elastic field radiated by the supercritically moving load is confined in a spiral-like apex. The membrane displacements at the boundaries of this apex are discontinuous. The radiated energy per period of load rotation is calculated showing a discrete energy spectrum. For increasing load velocities, the total amount of radiated energy becomes larger. It also turns out that the major part of the radiated energy follows the direction of the load motion.