Abstract Pentamode metamaterials are artificial structural materials designed to control the propagation of waves with specific frequencies and modes which possess both solid morphology and fluid properties. Thus, they have important applications in underwater acoustic wave modulation. As acoustic wave detection technology continuously expands research into the low frequency band, designing pentamode metamaterials with low frequency characteristics has become one of hot topics. In order to study the influence of anisotropy on the low-frequency acoustic characteristics of three-dimensional PMs, this work breaks the spatial structure symmetry of locally resonant PMs by changing the spatial position of the intersection points of the primitive elements, and uses the finite element algorithm to study its low frequency acoustic characteristics such as energy band characteristics and quality factor. The simulation results show that the introduction of anisotropy can open the first phonon band gap of three-dimensional pentamode metamaterials below 120 Hz. As the anisotropy increases, the working frequency band in the single-mode region shifts towards lower frequencies. The figure of merit can be increased 79.7% at most，the single-mode relative bandwidth can be increased 98%, and the first phonon band gap can be increased 500%. This research can provide guidance for designing low frequency three-dimensional pentamode metamaterial acoustic cloaks which based on acoustic transformation theory.
Cai et al. (Thu,) studied this question.