We study the substrate effect on the band gaps of lower-order Lamb waves propagating in thin plate with one-dimensional phononic crystal layer coated on uniform substrate. The transmitted power spectra are calculated by using the finite element method (FEM). The results show that when the substrate is hard, the influences on band gap are significant and the band gaps disappear rapidly as the substrate becomes thicker. However, when the substrate is soft, the depth of band gaps becomes larger as the thickness of the substrate increases. A virtual plane wave expansion method is developed to calculate the dispersion curves of Lamb wave. The locations and widths of band gaps on the dispersion curves are in good agreement with the results from the transmitted power spectra by FEM.
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