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.

In this paper, the conventional rigorous coupled-wave analysis (RCWA) method is improved by using the Cayley-Hamilton theorem. Using the proposed method, the forward and backward diffraction efficiencies of each order are solved directly from the eigenmatrix. At the same time, the calculation results of the conventional method, the proposed method, and the CST simulations are in good agreement with each other. The results show that the proposed method has obvious advantages in computational efficiency.

For high efficient analysis of an obliquely incident plane wave on periodic structures, one-step leapfrog locally one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed in this letter. Firstly, by applying the LOD scheme into the improved split-field algorithm, unconditional stability can be achieved. And then, by introducing three auxiliary variables, the one-step leapfrog implementation for the LOD scheme is derived. Finally, the implementation of the convolutional perfectly matched layer (CPML) for the proposed method is derived. At last, numerical results are given to verify the accuracy and efficiency of the proposed method.

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.