Time-average holographic estimation of Poisson's ratio by Cornu's method from mode shapes
More than 150 years ago, Marie Alfred Cornu first demonstrated his method of using interferometry to directly measure Poisson’s ratio from a radially bent beam. It is an elegant approach to measuring Poisson’s ratio of a beam requiring only two length measurements. Cornu’s method combines the high precision of interferometry with a four-point bending apparatus. This research simulates an interferometry technique called time-average scanning digital holography to make direct estimates of Poisson’s ratio from the antin odes of a mode shape. We show it is possible to make direct estimates of Poisson’s ratio from the antinode of a mode shape although the estimates diverge from the true value of Poisson’s ratio. We find that the di vergence is proportional to the distance between the nodes of a mode shape. We then develop an expression for converting our direct estimate back to within two percent of the true value of Poisson’s ratio for a thin, homogeneous, and hinged-hinged beam, or plate. The remainder of the research seeks to extend this method to combinations of clamped, free, and hinged boundary conditions.