FORCED MOTIONS OF TIMOSHENKO BEAMS

Abstract

In attempting a complete solution for the general forced vibration problem, the homogeneous differential equations of motion (with homogeneous boundary conditions) were set up for the free vibrations of beams. These equations were satisfied for an infinite set of discrete frequencies each of which corresponds to a mode shape. Rayleigh's method (Theory of Sound, p. 262, Dover Publications, N. Y., 2nd ed., 1945) was then used to formulate the orthogonality property for the principal modes of free vibration. By using these results and the procedures of Mindlin and Goodman (Am. Soc. Mech. Eng. Paper 49-A-19, 1949) for time-dependent boundary conditions, the general problem of forced motion was reduced to a free vibration problem and a quadrature.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1953
Accession Number
AD0013062

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  • G. Herrmann

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  • Columbia University

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  • Ground and Sea Platforms

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  • Aeronautical Engineering
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  • Calculus or Mathematical Analysis
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