Supplemental Material for "Dual-band topological rainbow Trapping and frequency separation in two-dimensional elastic phononic crystal"

See supplementary materials for unit cell band structures with different structural parameters and a more refined rainbow capture phenomenon. Focus on discussing the impact of structural parameters on the first, second, and third band gaps. Also discuss the change in rainbow capture frequency after reducing the gradient parameter. After reducing the gradient, the capture frequency is refined to approximately 5 Hz.