Acoustically induced vibration of, and sound radiation from, slender beams

Abstract

This thesis deals with the acoustic coupling between slender beam structures and a surrounding fluid medium. The sound radiated from an unbaffled slender cylindrical beam vibrating transversely at resonance is calculated by solution of the classical wave equation subject to the boundary conditions imposed by the motion of the beam. The relationship between sound radiation and acoustically induced vibration is then demonstrated by using a theory based upon the principle of reciprocity to predict the resonant response of a cylindrical beam to acoustic excitation. The results show that radiation and response are highly dependent on frequency and the ratio of structural to acoustic wavelengths.

An idealized acoustic source model for a transversely vibrating beam is established by calculating the sound pressure radiated to the far-field. The results show that a vibrating beam can be represented as a line of coupled dipole sources.

For periodically supported beams an exact solution of the wave equation is seen to be extremely difficult with the boundary conditions imposed by the complex mode shapes. Approximate solutions are obtained by defining an effective structural wavelength for sound radiation. These approximations are sufficiently accurate for use in design.

Experimental measurements of sound radiation and response have involved consideration of the statistical parameters which control sound and vibration measurements in a reverberant room. It has been shown
that reliable measurements of the radiation resistance of an extended, source such as a vibrating beam can be made at a single point if the length of the source is longer than an acoustic wavelength, and if many microphone positions are used to determine the mean sound pressure level. This result has been utilized in an extensive experimental programme.
The radiation resistance and pure-tone acoustic response of three freely- suspended and three periodically supported beams have been measured in a large reverberant room. The experimental results agree well with theoretical predictions.

An experimental programme has also been conducted in a large anechoic room. Measurements have been made of polar directivity and the wavelength coincidence effect which occurs when a plane wave impinges on a structure at an angle such that the acoustic trace wavelength is equal to the bending wavelength of the structural mode.

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