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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(1):97-108; doi:10.1093/qjmam/5.1.97
© 1952 by Oxford University Press
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A CRITICAL EXAMINATION OF THE REPRESENTATION OF MASSIVE AND ELASTIC BODIES BY SYSTEMS OF RIGD MASSES ELASTICALLY CONNECTED

W. J. DUNCAN

( Department of Aeronautics and Fluid Mechanics, The University Glasgow )

It is shown that, when the mass of an elastc body of linear form is supported to be condensed into rigid masses to particles situated at the mid-points of equal segments while the elastic properties of the body are unaltered, the error in the frequency of any natural mode of oscillation ultimately varies inversely as the square of the number of segments. When the mass are not placed at the midpoints of the segments the error varies ultimately as the inverse first power of the number of segments. The general conclusions are checked by numerical examples and by comparison with cases where exact solutions for the semented bodies are available.


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