Effect of anisotropy on phononic band structure and figure of merit of pentamode metamaterials

We propose herein four types of anisotropic pentamode metamaterials (PMs) created by shifting the thin-end contention points along the space-diagonal, x-axis, y-axis, and z-axis directions. The phononic band structure and figure of merit (FOM) of the four types of anisotropic PMs are systematically investigated by using the finite-element method. Compared with isotropic PMs, the first phononic bandgaps appear in low-frequency regions, and the FOM increases by a factor of 6.9 when the thin-end connection area shifts along the z-axis direction. This study investigates how anisotropy affects PM properties and provides a reference to design acoustic cloaks, acoustic waveguides, and acoustic barriers.