**4.1 Forming mechanisms of the lower frequency complete BGs**

In order to study the physical mechanism for the occurrence of the lower frequency complete bandgap in the metal-matrix embedded phononic crystals [14, 18], several specific resonance modes (mode *A1*, mode *S1*), which correspond to the lower edge of the first bandgap (out-of-plane and in-plane bandgap), and several specific traditional plate modes (mode *A2*, mode *S2*), which correspond to the upper edge of the first bandgap (in-plane and out-of-plane bandgaps), are extracted.
