Application of the Electronic Differential Analyzer to the Oscillation of Beams, Including Shear and Rotary Inertia

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Abstract
The equations for normal modes of lateral vibration of beams are set up on the electronic differential analyzer. Beam deflections due to transverse shear and rotary-inertia forces are included. The differential analyzer is shown to be a fast and accurate method for solving the problem. Analyzer outputs include mode shape, slope, bending moment, and shear force along the beam. Curves showing the normal-mode frequencies for the first three modes of vibration of a uniform free-free beam are presented for a wide range of transverse shear and rotary-inertia parameters. The electronic differential analyzer also is utilized to solve the problem of lateral vibration of nonuniform beams.

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