Abstract
Stability problems of 2nd order time-varying damping system, which has the characteristic eguation of the form
d2θ/dz2+(k1+k2sinz)dθ/dz+pθ=0,
are investigated using Hill's method.
At first, it is shown that Hill's method is applicable without any modification to the extended Hill's eguation having not only cosine terms but also sine terms. Further, the means to find the stable and unstable regions in parameter space of k1, k2 and p, using digital computer, are shown.
As the results of this analysis, it is clarified that the time-averaged damping coefficient k1 and stiffness p must not be negative for necessary condition of stability, and that, even if k1 is positive, the system can be unstable in the vicinity of p=0.25 by the effect of time-varying damping coefficient k2 when approximately |k2|>2k1.
