RESPONSE SOLUTIONS FOR THE VIBRATION OF A TRAVELING STRING ON AN ELASTIC-FOUNDATION

This Tech Brief presents solutions to the response problem for the vib ration of an axially-moving string that is supported by an elastic fou ndation. This system is of technical interest in the area of flexible media which translates at a high speed, and which is guided by air bea rings or similarly modeled distributed supports. The equation of motio n is dispersive and contains askew-symmetric ''Coriolis'' acceleration component which derives from axial translation of the string. The equ ation of motion is written in the standard form for a continuous gyros copic system, so that the string's stability and response can be analy zed within this broader context. Available modal analysis and Green's function methods then provide closed form expressions for the response to arbitrary initial conditions and excitation.