Underwater acoustic stealth has great scientific research value. According to acoustic coordinate transformation theory, the acoustic stealth cloak based on pentamode materials can realize underwater broadband acoustic stealth. However, due to the correlation between the density and modulus of pentamode materials and the changes in the parameters of each layer of the acoustic stealth cloak, a large amount of structural optimization work is required for the pentamode material to meet the specific parameter requirements, which significantly increases the difficulty of the pentamode acoustic stealth cloak design. To simplify the design process, inspired by the calculation of equivalent modulus by representation volume element, this article proposed a pentamode material configuration with independent variation of density and modulus and designed a 1 m radius acoustic stealth cloak with a specific structure of pentamode materials matching the coordinate transformation equation of constant modal mapping. After simulation calculation and optimization design, in the range of a/λ from 0 to 1, the average total scattering cross-section of the cavity with a radius of 0.5 m covered by the acoustic stealth cloak is 0.858; the average total scattering cross-section of the cavity is 19.718 after removing the pentamode material acoustic stealth cloak. The results of the study are expected to provide some method references for simplifying the design process of the pentamode material acoustic stealth cloak and the microstructure design of the pentamode materials.

This study investigates the low-frequency vibro-acoustic characteristics of a finite locally resonant (LR) plate. A dynamic model of the finite LR plate consisting of periodic arrays of beam-like resonators attached to a thin aluminum plate with simply supported boundary conditions is established, and the average vibration response and radiated efficiency are theoretically determined by using modal-superposition and harmonic-balance methods. In addition, the study investigates the influence of the parameters and number of additional resonators on the vibro-acoustic performance of the finite LR plate. Finally, a vibration experiment of a finite plate with 8 × 10 uniformly distributed beam-like resonators validates the theoretical analysis results. The numerical and experimental results show that the finite LR plate has a low-frequency bandgap that can suppress the vibration and radiated noise of the structure, and the bandgap position is close to the resonance frequency of resonators. The position and performance of bandgaps can be influenced by changing the parameters and number of resonators. The experimental results show a bandgap ranging from 370 to 425 Hz, which is consistent with the theoretical prediction. The finite LR plates proposed in this study can find potential applications in the attenuation of low-frequency vibration and noise.

Pentamode materials have broad application prospects in the control of underwater elastic waves. It is of great significance to design pentamode materials configuration with certain compressive resistance to promote the underwater application of pentamode materials. Based on the particle swarm optimization algorithm, a multi-objective optimization design method considering structural pressure resistance is proposed. The optimization objective consists of three parts: pentamode attribute matching degree, underwater compression ability test, and target density and target modulus matching degree. Aiming at the octagonal frame structure with a fan-shaped mass block in the inner corner, the multi-objective optimization design method is adopted to optimize the thickness of the frame wall t, the radius of the mass block R, and the limit lengths l2 and h2. After optimization, the pentamode attribute matching degree of the material is 0.998. When the safety factor is equal to 1.5, it can withstand the hydrostatic pressure of more than 200 m water depth. In the frequency domain of 3 K to 6 kHz, the average value of the total scattering cross-section of the material is 0.055, which is similar to the sound propagation in pure water. The research shows that the multi-objective optimization design method of pentamode materials can be used to design the configuration of pentamode materials considering both underwater pressure resistance and sound transmission performance. The research results are expected to provide a method reference for the configuration design of underwater pressure-resistant pentamode materials.

Honeycomb material is one of the basic structures of two-dimensional pentamode materials. Dispersion curve, as a common method for analyzing crystal properties, is widely used in the study of pentamode materials. It is necessary to study the probability that using dispersion curves to calculate the equivalent parameters of honeycomb materials. In this paper, compared with the improved Gibson formula, the accuracy of the equivalent parameters calculated by dispersion curves of honeycomb pentamode materials with different structures is studied. The study found that the calculation error of dispersion curve for the homogeneous material equivalent parameters is lower than 1%; The error for anisopathic honeycomb pentamode materials is 10% to 20%, and it decreases with the ratio of wall thickness to edge length; Calculating anisotropic honeycomb pentamode material equivalent parameters by dispersion curves is inapplicable. But dispersion curves can be used to predict the degree of anisotropy of honeycomb materials, such as the ratio of volume modulus in the X and Y directions, with less than 5% errors.