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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(1):74-78; doi:10.1093/qjmam/10.1.74
© 1957 by Oxford University Press
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VIBRATIONS OF BEAMS

II. TORSIONAL MODES

W. A. GREEN

( University College of Wales Aberystwyth )

The second order perturbation method developed in the previous paper (1) is adopted for the consideration of torsional waves in a bar of general section. The determinantal froquoncy equation is obtained correct to second order, for the first mode of torsional oscillations of the bar. This equation is solved for particular wavelengths and dispersion curves sketched for bars whose sections approximate to a square, rectangle, and ellipse. As in the longitudinal case it is found that the method breaks down for the rectangle and the ellipse at a certain point due to degeneracy between the torsional and screw modes.


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