Thin Copper Strips Research Articles

Determination of Elastic Constants and Decrements from the Resonances of a Free Bar

An electrodynamic method of initiating and detecting, independently, the flexural, longitudinal, and torsional vibrations of a free bar is described. A thin copper strip is attached to each end of the bar. The three types of vibrations are determined by the permanent-magnet configuration, which is placed close to the copper strip. This carries an alternating current for the driver; while for the receiver the voltage induced in the strip is measured. It is shown how the logarithmic decrement of the bar material, as well as the elastic constants, can be calculated from the test results. An outline of an approximate theory is given. It is easy to obtain and predict corrections that are within 2% of the more-rigorous correction factors for flexural vibrations of rectangular bars. Tables of correction factors are provided for bars having thickness-to-length ratios from 0 to 0.30 and Poisson's ratios from 0 to 0.45 for the first three modes of vibration.