Measurement of the shear wave speed in a submerged plate

This paper develops an inverse method to estimate, in water, the shear wave speed in an isotropic, thick, elastomeric plate. The submerged plate is mechanically shaken and a scanning laser vibrometer is used to measure normal velocity on one surface. The temporal domain measurements are transformed into the frequency domain using a Fourier transform, then, the spatial domain measurements are transformed into the kx,ky wavevector domain using two Fourier transforms. Once the data is in the wavevector-frequency domain, the propagation wavenumber of each specific wave type can be estimated by fitting a circle to each collection of spectral peaks. Using this measured estimate of the wavenumber corresponding to the propagating wave, the Newton-Raphson gradient method is applied (inserting the estimated wavenumber into to the theoretical dispersion curve equation for wave propagation in a fluid-loaded plate,) hence resulting in an estimate of the shear wave speed. An experiment is included to illustrate the method and statistical properties of the measurement are discussed.