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The damage localization accuracy of a Lamb wave detection method is greatly influenced by the multi-mode character and the dispersion effect of Lamb waves. Warped frequency transform (WFT) with a warping function derived from the frequency-dependent phase velocity can be used to suppress the dispersion. Step-pulse excitation is adopted in this paper and the transfer function of the propagation path is extracted from the step-pulse response. WFT is then used to compensate the transfer function, and the compensation of the narrowband signal is realized by convolution of the ideal narrowband burst signal with the compensated transfer function. Considering that wavenumber is a key parameter in designing the warping function for compensation, we presented a method in this paper to calculate the wavenumber directly from the measured signal. This method uses the phase response to estimate the curve of wavenumber. The WFT method is then combined with the delay-and-sum Lamb wave imaging method to improve the imaging resolution. A comparison with traditional delay-and-sum method and time-reversal method verifies the effect of this method in improving the damage localization results. It is shown that the proposed method leverages dispersion to enable good performance in the presence of multiple modes.

Based on the first-order Taylor expansion, an efficient Rigorous Coupled-Wave Analysis (RCWA) for one-dimensional ultrathin periodic structures is proposed in this paper. The derivation of the ultrathin form RCWA method is completed by using the first-order Taylor expansion to rearrange the matrix in the equations of boundary conditions. Then, the reliability of the proposed algorithm is verified by two examples. Finally, it is concluded that the proposed algorithm can reduce the CPU time of TE polarization and TM polarization by more than 50%. Meanwhile, compared with the conventional algorithm, the proposed algorithm also needs less memory.INDEX TERMS RCWA, eigenvalues and eigenvectors, computational efficiency, ultrathin periodic structures.

For the purpose of improving the damage localization accuracy, a prewarping technology is combined with step pulse excitation and this method is used in Lamb wave imaging of plate structures with adjacent damages. Based on the step pulse excitation, various narrowband or burst response can be derived by signal processing technology and this method provides flexibility for further prewarping approach. A narrowband signal warped with a preselected distance is then designed, and the dispersion in the response of this prewarping signal will be greatly reduced. However, in order to calculate the distance for prewarping, the first arrival needs to be estimated from the burst response. From the step-pulse response, narrowband responses at different central frequencies can be obtained, and by averaging peak-value time of their first arrivals, a more accurate estimation can be calculated. By using the prewarping method to the damage scattering signals before imaging, the imaging resolution of the delay-and-sum method can be highly enhanced. The experiment carried out in an aluminum plate with adjacent damages proves the efficiency of this method.

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