Two-dimensional ternary locally resonant phononic crystals with a comblike coating

Two-dimensional ternary locally resonant phononic crystals used to consist of cylindrical scatterers with uniform coatings in their exterior. An alternative coating scheme with a comblike profile is proposed and investigated in this letter. The band structures are calculated by using the finite element method. It is found that a complete bandgap at a significantly low frequency can be induced. The mechanism for such a change is suggested by using an equivalent spring-mass model based on analyzing the eigen modes at the bandgap edges. Consistent results are obtained from the numerical results and the analysis of the spring-mass model.