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 band-gap characteristic is an important feature of acoustic metamaterials, which has important theoretical and practical significance in acoustic devices. Pentamode metamaterials (PMs) with phonon band-gap characteristics based on an asymmetric double-cone outside profile are presented and studied in this paper. The phonon band structures of these PMs are calculated by using the finite element method. In addition to the single-mode band-gaps, the complete 3D band-gaps are also obtained by changing the outside profile of the double-cone. Moreover, by adjusting the outside profile and the diameter of the double-cone to reduce the symmetry of the structure, the complete 3D band-gap can be widened. Further parametric analysis is presented to investigate the effect of geometrical parameters on the phonon band-gap property, the numerical simulations show that the maximum relative bandwidth is expanded by 15.14 times through reducing the symmetry of the structure. This study provides a possible way for PMs to control elastic wave propagation in the field of depressing vibration and noise, acoustic filtering and acoustic cloaking.

This study used the finite element method to investigate the acoustic bandgap (ABG) characteristics of three-dimensional pentamode metamaterial (PM) structures under the thermal environment, and a method for controlling the PM ABG based on external temperature variation is also proposed. The results indicate that the complete acoustic bandgap can be obtained for a PM in the thermal environment, which makes the PM combine the bandgap characteristics of phononic crystals. More than that, the bandwidth and locations of ABGs can be effectively manipulated by controlling the temperature. Considering the softening effect of thermal stresses, the ABG gradually moves to lower frequencies as the temperature increases. Based on this, different degrees of ABG tunability can be achieved by changing the thermal environment to propagate or suppress acoustic waves of different frequencies. This work provides the possibility for PMs to realize intelligent regulation of the bandgap.

Acoustic metamaterials have been widely applied in fields such as sound insulation and noise reduction due to their controllable band structures and unique abilities to manipulate low-frequency sound waves. However, there exists a highly nonlinear mapping relationship between their structural parameters and performance responses, which causes traditional design methods to face the problems of inefficiency and poor generalization. Therefore, this paper proposes a bidirectional modeling framework based on deep learning. We constructed a forward prediction network that integrates an attention mechanism, a multi-scale feature fusion, and a reverse design model that combines an improved autoencoder and cascaded neural network to efficiently model the dispersion performance of acoustic metamaterials. In the feedforward network, the improved forward prediction model shows superior performance compared to the traditional Convolutional Neural Network model and the model based only on the Convolutional Block Attention Module attention mechanism, with a prediction accuracy of 99.65%. It has better fitting ability and stability in the high-frequency part of the dispersion curve. In the inverse network part, compression of the high-dimensional dispersion curves by an improved autoencoder reduces the training time by about 13.5% without significant degradation of the inverse prediction accuracy. The proposed network model provides a more efficient method for the design of metamaterials.