New Method of Calculating Natural Modes of Coupled Bending-Torsion Vibration of Beams

Abstract

Abstract Recently the author developed a new method of calculating natural modes of uncoupled bending vibration of beams, the present paper being an extension of this work to take care of coupled bending-torsion vibrations as well. This latter problem has lately taken on considerable importance as a means of interpreting ground-vibration tests on airplane wings, which may be considered as a symmetric beam with free ends. The author’s method also makes it possible to consider the entire airplane as an elastic body both in symmetric and in antisymmetric vibration, and to find the effective inertia of an airplane propeller in determining the torsional vibration characteristics of the engine. It may be readily applied to the vibration of turbine blades and propellers in general, when the centrifugal force is taken into consideration. This method possesses the advantage that the computations may be performed by inexperienced calculators as only the routine completion of a tabular form is required.