Vibrations of and sound radiation from some periodic structures under convected loadings

Abstract

This thesis deals with the forced, vibrations of infinite periodically supported beams, orthogonally stiffened plates and ring stiffened cylindrical shells excited by random convected loadings. The sound power radiated under these conditions is also dealt with. The stiffened structures are represented by uniform beams, plates or shells on periodically spaced elastic supports which represent stiffener-skin interaction forces and moments. The available literature on the response of stiffened structures is first reviewed. A special infinite series of space harmonics is then evolved and employed to obtain the response of infinite stiffened beams, plates and cylindrical shells to spatial and temporal harmonic loadings. The coefficients of this series are determined by applying the principle of virtual work. The series is shown to be satisfactorily converging so that only a limited number of terms need be included for an actual solution of a reasonable accuracy. The method easily predicts and explains the sound radiation by structures excited by loadings convected at subsonic convection velocities. The terms in the series contributing to this radiation can be easily identified with the help of a simple diagram included in the thesis. The response to boundary layer pressure field has been obtained by analysing this field into a wave length frequency spectrum and then numerically integrating the response due to each wave length component. The low wave numbers in the spectrum are important for sound power radiated by the structure especially at subsonic convection velocities of loading. An experiment has been carried out to determine the sound power radiated by an orthogonally stiffened damped panel representative of aircraft construction under excitation by acoustic plane waves. A satisfactory agreement has been obtained between experimental and theoretical results.

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