Topological insulators are a research hotspot due to their unique properties of backscattering immunity and defect insensitivity for edge states propagating on the complex boundaries. The analogues of valley states in electronic systems have recently led to acoustic valley Hall topological insulators. Acoustic valley edge states often exist on the domain walls between two phononic crystals that have different nonvanishing valley Chern indices, which are implemented by rotating the identical primitive unit cells. The restriction on using the same primitive unit cells in previous works does not show the realization of aperiodic valley topological insulators. We construct various configurations composed by two or more differently shaped primitive unit cells. Valley edge states are both numerically and experimentally demonstrated with the robust selection of $C_{3v}$-symmetric scatterers in adjacent domains. We also experimentally demonstrate the valley-selective cross-waveguide beam splitter by measuring the transmission spectra. The robust selection of $C_{3v}$-symmetric scatterers in this work may provide more possibilities for designing alternative acoustic-topological-insulator-based devices with flexible structures.

A new phononic crystal with the graded supercell configuration is proposed to broaden the Bragg scattering band gaps. The graded structural design can merge adjacent multiple band gaps into an extremely broad one. The proposed phononic crystal is made up of a periodic arrangement of supercells, and the supercells are composed of unit cells with graded structural parameters. The mechanical model of the graded phononic crystals is established based on the transfer matrix method to investigate in-plane elastic waves propagating and band structures of the periodic system. Modal analysis shows that the mechanism for the broadening of band gap is that the graded supercell configuration breaks some symmetries of the phononic crystal, resulting in the opening of the Dirac cone and creation of new band gaps. The effects of the main structural parameters related to graded supercell design on band gap broadening are studied by simulation and verified by the experiment. The present study is beneficial to the design of new functional materials with broadband vibration isolation performance.

Recently, the field of topological acoustics has rapidly developed, where the topological phase transition in phononic crystals is unveiled to occur through band inversion via the Dirac degeneracy in momentum space. Here, we focus on a class of low-symmetry acoustic valleylike topological insulators (VTIs), with honeycomb-lattice scatterers being chiral with $C_1$ symmetry. The valley Hall transition can be generated by simply rotating the chiral scatterers, where the topological phase transition is triggered by reopening the Dirac degeneracies beyond high-symmetry points and boundaries in the Brillouin zones. We numerically and experimentally demonstrate robust transport against different defects in chiral VTIs. For applications, we construct a topological beam splitter to verify the valley-selective one-way transport in chiral VTIs. Based on valleylike edge states, we design a topological acoustic switch with one input and two outputs, where the switching functionality at outputs with the on-off, off-off, and off-on states is confirmed by simulations and experimental tests. We also provide a more complex four-port acoustic switch based on chiral VTIs. The chiral VTI-based splitter and switches may have potential applications in constructing intelligent acoustic devices.