In this paper, the phononic band structures of Bragg scattering and locally resonant pentamode metamaterials (PMs) with single and composite materials symmetric double-cone elements (SDCEs) are calculated by using the finite element method. The numerical results show that, for the Bragg scattering PMs with single material SDCEs, the phononic band gaps (PBGs) can be obtained while the top touch cone diameters (TTCDs) (i.e. d ) are much smaller than the bottom touch cone diameters (i.e. D ), and the variation range of the PBGs frequency is mainly determined by the TTCDs. This indicates that the Bragg scattering PMs with single material SDCEs can be investigated as a phonon crystal. On this basis, the locally resonant SDCE PMs can be designed by using the composite SDCEs instead of single material SDCEs, and the PBGs can be obtained under the 100 Hz. This finding provides a way to control the low-frequency acoustics waves by using small-sized SDCEs PMs. In addition, compared with the Bragg scattering PMs, the relative bandwidth of the first PBGs of the locally resonant PMs can be expanded at least 25 times. In the end, the effect of mass density ρ and Young’s modulus E of the composition material parameters of locally resonant SDCEs PMs on the PBGs is also studied by changing the parameters individually. The results show that the lower and upper edge and relative bandwidth of the first PBGs of locally resonant PMs with composite SDCEs are mainly impacted by the difference of the mass density ρ between the two constituent materials, and the difference of the Young’s modulus E between the two constituent materials has little effect on the PBGs.

Locally resonant phononic crystals have excellent low-frequency characteristics and can result in a small size controlling a long wavelength. Based on the locally resonant phononic crystal theory, locally resonant pentamode metamaterials with composite materials are proposed and studied. The acoustic band frequencies of the locally resonant pentamode metamaterials were found to be two orders of magnitude smaller than those of conventional Bragg-Scattering pentamode metamaterials with the same lattice constant. Therefore, the single-mode frequency regions and locally resonant acoustic bandgaps which are under 110 Hz can be obtained by locally resonant pentamode metamaterials with a centimeter-scale lattice constant. The figure of merit can be increased by 60.78%–138.08%. This kind of locally resonant pentamode metamaterial opens a new path for applications in low-frequency acoustic cloaking and control of long wavelengths using small structure dimensions.

The method for tuning the first phononic band gaps (PGBs) of locally resonant pentamode metamaterials (PMs) is proposed in this paper. Based on the equivalent relationship between the locally resonant mode at the lower edge of the first PBGs and spring-mass system, the approximate relationships between the lower edge of the first PBGs and structure parameters are obtained. The theoretical and numerical results show that the first phononic band gaps of PMs can be tailored between 52 Hz and 548 Hz by a small-sized PMs. In addition, the single mode PBGs of PMs can be expanded by 6.5 times, and the pentamodal characteristics can be improved by 13.7 times.

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.

The integration of multiple functionalities into a single, planar, ultra-compact metasurface has presented significant opportunities for enhancing capacity and performance within compact 5G/6G communication systems. Recent advances in multifunctional metasurfaces have unveiled comprehensive wavefront manipulations utilizing phase, polarization transmission/reflection, and coding apertures. Despite these developments, there remains a critical need for multifunctional metasurfaces with expanded channel capabilities, including multiple operational frequencies, minimal crosstalk, and high-efficiency computable array factors. This study introduces a multifunctional metasurface that integrates phase- and amplitude simultaneous coding meta-atoms at dual frequencies. By altering the polarization of electromagnetic (EM) waves, it is possible to reshape the wave-fronts of reflected waves at these frequencies. The coding metasurface proficiently manipulates both x and y linearly polarized waves through phase and amplitude coding at dual frequencies, thereby enabling distinct functionalities such as anomalous reflection, reflection imaging, and vortex wave beam generation. Both theoretical analysis and full-wave simulation confirm the anticipated functionalities of the designed devices, paving the way for advancements in integrated communication systems with diverse functionalities.

In this paper, we propose a class of pentamode metamaterials for which the frequency range of the acoustics band gaps can be tuned and large figures of merit can be obtained. The band structures of the pentamode metamaterials are calculated systematically by using the finite element method. The numerical results show that the lower edge frequency of the first acoustics band gaps of pentamode metamaterials can be tuned between 3.72 kHz and 10.6 kHz by changing the diameters of the bottom and top touch cones slightly, and the relative bandwidth of the first acoustics band gaps can also be expanded. In addition, compared with the results seen in the previous research in this area, the volume filling fraction of pentamode metamaterials can be decreased by 15.7%–24.4% and the maximum figure of merit can be increased by 39.2%.