Method for measuring shear wavespeed in an isotropic plate
View Patent ↗Using a mechanical shaker test the shear wavespeed in a plate is estimated by applying a cyclical point force to the plate, measuring normal velocity of waves caused by the force, transforming temporal domain measurements with a Fourier transform into a frequency domain, transforming spatial domain measurements into a {k x ,k y } wavevector domain spectra using Fourier transforms, determining propagation wavenumbers for given Lamb waves from peaks within the {k x ,k y } spectra, and determining shear wavespeed by applying a Newton-Raphson gradient method using the propagation wavenumbers to Raleigh-Lamb dispersion curve equations.
1. A method to measure a shear wavespeed of waves in an isotropic plate, comprising the steps of:
providing the isotropic plate in a manner to minimize dynamic mounting forces;
applying a time cyclical point force having a known frequency and magnitude to the plate to initiate waves in the plate;
measuring normal velocity of the waves as a temporal domain measurement in a spatial domain on a first planar surface of the plate;
transforming the temporal domain measurement into a frequency domain;
transforming the frequency domain measurements into a {kx, ky} wavevector domain spectra using two Fourier transforms, one transform for each dimension, kx and ky;
determining propagation wavenumbers for given Lamb waves from peaks within the {kx, ky} wavevector domain spectra; and
determining a shear wavespeed of the waves in the plate by using the determined propagation wavenumbers, wherein propagation wavenumbers are determined by applying a Newton-Raphson gradient method to Raleigh-Lamb dispersion curve equations.
2. The method of claim 1 wherein said normal velocity of the waves is measured utilizing a scanning laser vibrometer.
3. The method of claim 1 wherein said time cyclical point force is applied at frequencies above about 1000 Hz.
4. The method of claim 1 wherein the step of determining a shear wavespeed is determined by:
fitting a circle to the relative maxima points;
determining the wavenumber k for a specific Lamb wave as a fitted radius of the circle;
estimating the square of the shear wavenumber from the wavenumber; and
computing the shear wavespeed from the square of the shear wavenumber.
5. The method of claim 4 wherein symmetric Lamb waves are used to estimate the square of the shear wavenumber.
6. The method of claim 4 wherein antisymmetric waves Lamb waves are used to estimate the square of the shear wavenumber.