Finite element solution to dynamic stability of bars.

treated in Ref. 1. Note that for this low-frequency mode, \I/N = 1 in (6), and the correcting series is proportional to the Mach number Mb. The series converges rather slowly, but since Mb ~ 0(10~), the deviation from spatial uniformity is indeed quite small. Thus, as Oberg emphasized, the nonacoustic instability is, in fact, a special form of acoustic oscillation. The main point of the remarks here is simply that by means of a thorough analysis giving Eq. (7), one obtains the useful results for frequency and growth constant, valid for any grain configuration and subject only to the weak constraint that the meanflow Mach number is small. Similar formulas can be obtained also for gas and liquid rockets. The principal difference from the solid rocket arises from the influence of combustion within the chamber and not merely at the boundary.