Experimental validation of an analytical method to predict lamb wave scattering from a discontinuity

This paper presents an experimental validation of an analytical method called complex mode expansion with vector projection (CMEP), which is used to calculate the scattering coefficients (amplitude of the out-of-plane velocity) of Lamb wave modes from geometric discontinuities. For a test case, a plate with a thickness step change type geometric discontinuity is considered in this paper. The scattered wave fields from the discontinuity are expanded in terms of complex Lamb wave modes with unknown scatter coefficients. These unknown coefficients are obtained by projecting the stress or displacement boundary conditions on the displacement or stress boundary conditions utilizing the power expression. In the analytical analysis, complex-valued scatter coefficients are calculated with frequency-thickness product from 50 to 1500 kHz mm for A0 incident wave. A parametric study was conducted using CMEP to find the optimized step depth ratio for the experiment. For incident A0 mode at step depth ratio of 0.6, the scattering coefficients of reflected and transmitted S0 modes are maximum. A plate of thickness 4.86 mm with a step depth ratio of 0.6 was chosen for experimental study. Long piezoelectric wafer active sensors (PWAS) were used to create straight crested Lamb wave modes. Antisymmetric Lamb wave mode selectively excited by using two PWAS in out of phase on opposite sides of the plate. Scanning laser Doppler vibrometer was used to measure the out-of-plane velocity of scattered Lamb wave fields on the plate. Scatter coefficients were calculated from Fourier transform of the time domain signal. The obtained experimental results agree well with the CMEP analytical predictions.

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