Abstract
The equations of motion for a beam with solid rectangular cross-section are derived from the displacement field of Rayleigh-Lamb plate theory. Cross-sectional properties, such as the dynamic moment of inertia, cross-sectional area and the radius of gyration of the cross-section, are investigated as functions of frequency. It was found that as the elastic surface wave in any medium converges to the Rayleigh surface wave in the limiting case of infinite frequency, the dynamic radius of gyration for a half-infinite medium can be defined in spite of being unbounded. The dynamic radius of gyration for the first mode of phase velocity in a beam in the case of infinite frequency converges to 68% of static values. The same radii converge to zero for modes of phase velocity higher than the second. This result indicates that only the first mode of phase velocity of a flexural wave survives on the surface of a beam medium as a Rayleigh surface wave in the case of infinite frequency.
