A Heuristic Model for Estimating the Lowest Gap of Locally Resonant Phononic Crystals

Abstract

The influences of the constituent material parameters of the three-dimensional locally resonant phononic crystal on the lower and upper edge frequencies of its lowest gap are investigated with the Multiple-scattering theory. It is found that the frequency dependence on those parameters can be well reproduced by a simple mass-spring model, which manifests the physical essence of the resonance modes determining the edge frequencies of the gap. Since the equivalent mass and stiffness of the model can be determined from the material parameters and structure size in one unit cell, the lower and upper edge frequencies of the lowest gap of locally resonant phononic crystals can be estimated from this model analytically. Comparison between the analytical estimations and the numerical results calculating with multiple scattering method shows very good agreement. The proposed heuristic model lends itself to understand the locally resonant mechanism more clearly. The frequency estimating formulas induced from the model allow one to predict the edge frequencies of the lowest gap, which simplifies the design process of locally resonant phononic crystals.