– The purpose of this paper is to propose a modal method to calculate the band gaps of one-dimensional (1D) phononic crystals.
– The phononic crystals have modes with exponential form envelope in the band gaps, however, outside the band gaps the modes are of amplitude modulation periodic form. Thus the start and end frequencies of band gaps can be determined from the existence conditions of periodic modes. So, the band gaps calculation of 1D phononic crystal is transformed into the existence discussion of periodic solution of mode shapes equation. The results are verified by finite element harmonic response analysis.
– At the start and end frequencies of the band gap, the mode equation have solution with period of lattice constant.
– Compared with the traditional theoretical methods, the proposed modal method has a clearer principle and easier calculation.
