Abstract
It is assumed that the blade rotates about a fixed axis with a constant angular velocity and that it is subjected to a known load parallel to the axis of rotation. The axis of the blade, which is a line through the centroid of each cross section, is not necessarily a straight radial line, but its deviation from such a line must be small. For each cross section, one of the principal axes of moment of inertia is also considered to be parallel to the axis of rotation and bending is assumed to take place in a plane through this axis. The load as well as the mass of the blade are concentrated at distinct points on the blade axis. Under these assumptions the proposed method of analysis will give the shear forces, bending moments, slopes, and deflections by performing a series of tabular calculations. The load, which is always periodic, must first be put in the form of a constant term and a series of harmonic terms, each of which must be analyzed separately. The effects of the constant load and the eccentricity and slope at the base of the blade axis are found together and are easily disposed of in two simple tabular calculations involving only real quantities. The effect of each harmonic involves three tabular calculations with complex numbers. The complex numbers take care of the phase angles which vary along the axis of the blade.
