Dynamic measurement and characterization of Poisson's ratio
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Poisson's ratio for aluminum is estimated from velocity proflle measurements of a free-free beam under dynamic loading conditions A weighted least-squares method is used to select a beam model which is subsequently used to determine the transverse and anticlastic radii of curvature. The model of the beam velocity profile is selected using forward regression with the possible regressor set formed by products of Legendre polynomials in x and y, the two-dimensional coordinates of the beam. The resulting model is manipulated to extract the transverse and anticlastic radii of curvature of the beam which are then used to find local and global estimates of Poisson's ratio. Estimates for Poisson's ratio are found for three different forcing frequencies and three force amplitudes at each frequency. The frequencies selected correspond to the frequencies of the operating shapes dominated by the flrst, second, and third bending modes. A statistical analysis is performed to assess the quality of the estimates of Poisson's ratio.
Results show that the estimates of Poissonfs ratio are dependent on the forcing frequency and forcing amplitude. All estimates are below the accepted value of .33 for aluminum. Contributions of plate modes adversely affect the estimates. Estimates based on the first and third operating shapes exhibit a lower variance than the estimate based on the second operating shapes.
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