A study of rotational critical speeds for a multi-mass system by influence coefficients

In this investigation an attempt has been made to determine the critical speeds of a multi-mass rotational system by using influence coefficients. Modes of vibrations are also examined at these critical speeds. A shaft carrying five masses, supported by bearings at the ends, has been studied analytically. The length of the bearings is considered small with respect to the shaft length and therefore, the configuration is assumed to be point supported as a simple beam. The five masses, each weighing one pound, were placed at equal distances of 10 inches on a 60 inch shaft. The critical speed was examined with the same load but for different radii of the shaft. The radius was constant for any given shaft but the radii were varied between shafts from 0.1 inch to 0.5 inch in increments of 0.1 inch. Increasing the radius of the shaft causes a corresponding increase in its weight and a definite relationship was obtained between radius and critical speeds. An IBM-1620 digital computer was used in this investigation because it is difficult to determine the critical speeds and deflection ratios of a multi-mass system without one --Abstract, page ii