A novel modal calculation method of 1-D phononic crystal band gap

Abstract

Purpose

The purpose of this paper is to propose a modal method to calculate the band gaps of one-dimensional (1D) phononic crystals.

Design/methodology/approach

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.

Findings

At the start and end frequencies of the band gap, the mode equation have solution with period of lattice constant.

Originality/value

Compared with the traditional theoretical methods, the proposed modal method has a clearer principle and easier calculation.

Citation

Li, L. and Liu, Q. (2015), "A novel modal calculation method of 1-D phononic crystal band gap", Multidiscipline Modeling in Materials and Structures, Vol. 11 No. 1, pp. 16-22. https://doi.org/10.1108/MMMS-11-2014-0057