A time-domain local radial basis function collocation method for the band structure analysis of 2D anti-plane phononic crystals

In this paper, a time-domain local radial basis function collocation method (LRBFCM) combined with the Houbolt method is developed for the anti-plane elastic wave propagation analysis in 2D phononic crystals. The periodic boundary conditions are applied to a unit-cell to simplify the analysis. In the first step, the timedependent displacement field is computed by using the proposed time-domain LRBFCM. Then, the Fast Fourier Transform (FFT) is applied to transform the displacement field from the time-domain to the frequencydomain, from which the frequency band structures can be further obtained. To enhance the stability of the proposed LRBFCM, the direct method is used to calculate the spatial derivatives arising in both periodicity and interface continuity conditions. The proposed time-domain LRBFCM provides an alternative numerical tool to many frequency-domain methods for the band structure analysis of phononic crystals.