A Theoretical and Experimental Investigation into the Spectra of Selected Resonators

Abstract

An acoustic transmission line system in which the echo returned from a resonator, having an arbitary spectrum of resonances has been analysed. The results show that the system, which is of practical importance because of the separation of the signal transducer and the resonator being studied, can be used for a variety of material measurements. The special case of a line resonator, which has an harmonic spectrum has been examined using Laplace transform technique, and the rigour of the solution is established by specific experimental tests. The approximations of classical accoustical theory which assumes a lumped rather than a distributed resonator and expresses material loss as a ‘Q’ factor have been reconciled to this exact theory. Contour vibrations of disk resonators were investigated and the results are compared with recent numerical solutions from theory. A variety of specimens in disk form were used to determine elastic constants and their temperature coefficients with high precision. The extension of the disk theory to cover anisotropic materials has been considered. The disk theory has been extended to include a second boundary - a concentric hole - and numerical solutions obtained. Results are in agreement with the well-established thin ring spectrum for large holes and disk theory for small holes, Experiments on the full range of hole sizes verify the results to the limit of experimental error. The theory for the line resonator was extended to show that it is a convenient resonator form for Internal Friction measurement. The material Q of a pure copper rod was measured over a wide temperature (iii) range and the results are in agreement with those of other workers. The electronic equipment developed for the various measurements is described briefly and the possible methods of automation are discussed.