STABILITY ANALYSIS OF AN AXIALLY ACCELERATING STRING

The dynamic response of an axially accelerating string is investigated . The time dependent velocity is assumed to vary harmonically about a constant mean velocity. Approximate analytical solutions are sought us ing two different approaches. In the first approach, the equations are discretized first and then the method of multiple scales is applied t o the resulting equations. In the second approach, the method of multi ple scales is applied directly to the partial differential system. Pri ncipal parametric resonances and combination resonances are investigat ed in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuat ions is close to two times the natural frequency of the constant veloc ity system or when the frequency is close to the sum of any two natura l frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabili ties are detected up to the first order of perturbation. Numerical res ults are presented for a band-saw and a threadline problem. (C) 1997 A cademic Press Limited.