Investigation of quasi-one-dimensional finite phononic crystal with conical section

In this paper, we studied the propagation of elastic longitudinal waves in quasi-one-dimensional (1D) finite phononic crystal with conical section, and derived expressions of frequency-response functions. It is found that, contrary to the 1D phononic crystal with a constant section, the value of attenuation inside the band gaps decreases quickly when cross-sectional area increases, and the initial frequency also decreases, but the cut-off frequency increases, thus the width of the band gap increases. The effects of lattice constant and the filling fraction on the band gap are also analysed, and the change trends of the initial frequency and cut-off frequency are consistent with those of constant section. It is shown that the results using this method are in good agreement with the results analysed by the finite element software, ANSYS. We hope that the results will be helpful in practical applications of phononic crystals.