Research on the Design of Phononic Crystal Rod Band Gaps Based on Lumped Mass Method

Phononic crystals are a kind of artificial functional composite materials with vibration band gaps, which has a wide range of applications in vibration and noise reduction as well as in mechanics. Phononic crystals are limited in engineering applications because of the difficulty in designing suitable structures according to the specified band gap. In this paper, a method of inverse parameter design based on the band gap of phononic crystal rod is proposed. Firstly, the periodic rod is discretized into spring oscillator structure by using the Lumped-mass method, and the relationship between dispersion polynomial and band gap is studied by combining Bloch’s theorem. It is observed that range and position of band gaps are inseparable related to the coefficient of dispersive polynomial. Then, the criteria of frequency point and frequency band of band gaps are proposed. Dispersive curves, longitudinal vibration band gaps, and transmission rate are numerically calculated and simulated. The results show that these criteria can meet the goal of the band gaps in assessing the vibration attenuation of the frequency point and frequency band research. Reliable theoretical calculation and simulation results. This work is expected to be helpful in the design and application of the band gap of phononic crystal rods.