In this work, we numerically and experimentally investigate topological rainbow trapping and energy amplification of acoustic waves in a gradient phononic crystal (PC) structure. Thanks to the acoustic valley Hall effect, topological interface states (TISs) are generated along the interface between two PCs with different topological phases. To achieve rainbow trapping, we introduce the gradient into a 3D-printed PC structure by varying the geometrical parameter of scatterers along the interface. The incident acoustic waves at different frequencies split, stop, and, hence, are significantly amplified at different positions. Notably, the rainbow trapping of TISs is immune to random structural disorders. The topological rainbow trapping is promising for the design of broadband energy harvesters with excellent robustness.

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