VIBRATIONS OF BALLOONING ELASTIC STRINGS

This paper investigates the nonlinear dynamic response of a linearly e lastic string fixed at one boundary and undergoing constant speed circ ular motion at the other boundary. The response divides into nonlinear steady-state ballooning that is fixed relative to a rotating coordina te system and linearized vibration about the steady state. Single-loop balloons have high tension and purely imaginary eigenvalues. The sing le-loop vibration frequencies generally decrease with increasing ballo on length. Highly extensible strings whirl in first and higher modes w ith forward whirling modes having lower frequencies. Axially stiff str ings exhibit whirling only in higher modes. If the nondimensional stri ngs stiffness is larger than 1000, then the inextensible steady-state solutions and the lowest six vibration frequencies match the extensibl e results to within three percent. One-and-a-half loop balloons are di vergently unstable. Long and/or sufficiently extensible strings form l ow-tension double-loop balloons. Inextensible double balloons are coup led mode flutter unstable. The steady-state balloons, steady-state eye let tension, and balloon stability are experimentally verified.