In this paper, a one-dimensional acoustical topology by energy hopping within power-law variable section waveguides (VSWG) is proposed, in which a topological phase transition occurs due to the energy in the basic unit hopping to the nearby unit with the same energy mode resulting that its energy band is closed first and then opened. This research can realize the enhanced sound energy at the topological interface state and further regulated sound energy on the basis of enhancing sound energy. The large open hole determine the wide frequency range where the designable topological interface state is constructed and the power-law of the curve of the structure can adjust the size of the common forbidden band of the two topological states, so as to further improve the bandwidth. The small open hole control the magnitude of the acoustic energy at the topological interface state. This research will provide guidance for designing acoustic devices with different frequencies, different acoustic energy concentrations and realizing engineering applications of other multifunctional acoustic devices.

For resonant-type absorbers with a back cavity, the improvement of low-frequency sound absorption always depends on increasing the back cavity depth, which hinders its practical application. To realize satisfactory sound absorption performance in low- frequency range (<500Hz) while keeping the depth of the back cavity unchanged, a membrane-cavity-grate (MCG) meta-structure is proposed. The specific physical mechanisms for sound absorption are analyzed from acoustic impedance and energy dissipate perspectives. Furthermore, some key parameters of the MCG unit cell are investigated to optimize the sound absorption performance. On this basis, a meta-structure with 6-unit-cell is proposed. Compared with the structure without the grating, the meta-structure can realize 20% improvement of the average sound absorption coefficient in the range from 300-700Hz with the back cavity depth and the structure size unchanged, which is verified by the high consistency between finite element simulation and acoustic impedance tube experiment results. This work provides a potential avenue for low-frequency noise reduction structure design.

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