Estimating material wavespeed using the wavenumber transform of rectangular plate mode shapes

Experimental modal analysis is often used to estimate the natural frequencies and damping of a material sample. While the geometry of the sample is often arbitrary, thin rectangular samples are easy to manufacture, model and test and therefore are commonly-used for these measurements. The roving hammer approach can be used to collect frequency response functions at a rectangular grid of points located on plate. Once the mode shapes have been estimated for the rectangular sample, the discrete wavenumber transform can be used to find the wavenumber spectrum of each mode. For simply-supported boundary conditions, the relationship between the mode shape and the modal wavenumber can be determined analytically using the length of the plate and the distance between zeros in the wavenumber spectrum. For the more realistic free-free boundary, no simple relationship holds. However, it will be shown that the wavenumber verse frequency curve can still be accurately estimated using thin-plate theory to minimize the error of the modal wavenumber at each of the modes. The wavenumber curve can then be used to obtain the material wavespeed.