Inexpensive technique for accurate determination of elastic properties by free decay in circular plates

Abstract

Rapid determinations of elastic modulus are often made in the lab by measuring the resonances of regular bars of the material. When this is done, the most accurate results are obtained by suspending the specimen with as close to free conditions as possible. A circular plate supported by a taut wire through a central hole behaves accurately as an annular plate with both edges free. For low-loss materials, 10–20 modes are easily detected with an inexpensive microphone when such a plate is struck. Furthermore, the analytical solution for a thick, annular plate can be programmed readily in computational tools such as mathcad, matlab, or mathematica. (Even for plates traditionally considered thin—thickness-to-diameter ratios less than 0.1—thin-plate theory can produce significant errors for higher-order modes.) The first two resonance frequencies can be used to determine the elastic modulus and Poisson’s ratio and the higher modes can be used to assess the uncertainty or to uncover anisotropy. The resonance frequencies can be measured with a fast Fourier transform spectrum analyzer and an understanding of the response of such an analyzer to a slowly decaying sinusoid. [Work supported by the Naval Sea Systems Command.]