FREE-WAVE PROPAGATION IN PERIODICALLY-SUPPORTED, INFINITE BEAMS.
Summary rept. 1 Jun-31 Dec 68,
SOUTHAMPTON UNIV (ENGLAND) INST OF SOUND AND VIBRATION RESEARCH
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The notion of propagation constants for the free harmonic motion of infinite beams on identical, equi-spaced supports is first reviewed. Expressions are then derived for the flexural propagation constants for beams on rigid supports which exert elastic rotational restraint, and also for beams on flexible supports. A beam on rigid supports has one propagation constant and a beam on flexible supports has two propagation constants for each frequency. Detailed consideration of the propagation constant leads to the conclusion that a freely-propagating harmonic flexural wave in such a beam must be regarded as a wave-group, having components of different wavelength, phase velocity and direction. The magnitudes of the components in some special cases are examined. The interaction between these groups and convected pressure fields is considered in qualitative terms. A mechanism is shown to exist whereby slow, subsonic convected pressure fields can generate flexural waves of supersonic velocity which can radiate sound. Author