Using the transfer matrix method we calculate the frequency dependence of the transmission of longitudinal elastic waves for a layered structure where the specific acoustic impedance of the layers with odd numbering follows a Gaussian distribution, while the inserted even layers have the same impedance as the propagation medium. The structure presents intervals of low-pass, band-stop, and band-pass. The characteristics of the bands depend on the number of layers, on the contrast between the maximum and minimum impedances of the structure, and on the ratio of the width of the inserted layers to the width of the layers with a Gaussian distribution of impedances.
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