For the first case, the dispersion diagram is shown in Fig 2. It is seen that there is nearly no band gap for 1cm cylindrical lead. When the diameter of the cylindrical lead is increased, it is seen that the complete gaps appear at 4000~5000Hz and 6800~8200Hz (Fig 2(b)). As suggested by the concept of multi-resonator acoustic metamaterial, the gaps can behave differently by considering more inner mass-spring system or adding more compliant layer between the cylinder and the matrix. Thus, we will also consider embed a fluid-like coating material between the lead cylinder and polyethylene to discuss the coating effect of the dispersion relation.