“…The proposed model possesses two adjacent 1D-PnCs. Each 1D-PnC consists of ternary periodic muffler tubes [28] with different cross-sections, as depicted in figure 1. The geometrical parameters of the first PnC (PnC1) are d 1 (thickness of the first layer), d 2 (thickness of the second layer), d 3 (thickness of the third layer), N (number of periods), S 1 (cross-section of the first layer), S 2 (cross-section of the second layer), and S 3 (cross-section of the third layer).…”