A novel arc-type auxetic cellular doubly-curved shells with negative Poisson's ratio for broadband low-frequency sound insulation

Abstract

The novel cellular cores auxetic metamaterials with negative Poisson's ratio (NPR) have unique mechanical deformation characteristics compared to conventional cellular cores, which can be further applied to modeling lightweight sandwich structures. The Arc-type cellular core is based on the traditional re-entrant cellular core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. Based on that, the sound transmission characteristics of sandwich doubly-curved shells with NPR arc-type auxetic cellular core layer is studied in this article. The Hamilton's principle is applied to derive the governing equations and considers fluid-structure coupling by applying normal velocities continuity conditions at the fluid-structure interface, which is further analytically solved using Navier's method, and the sound transmission loss (STL) is described analytically. The correctness of the proposed formula is verified by comparing the theoretical solution with the calculation results of the commercial software COMSOL and the experimental results of impedance tube sound insulation. Based on the theoretical model, it is calculated that the average STL of the arc-type cellular is 6.61% higher than that of the traditional re-entrant cellular within the broad low-frequency range of 100–2448Hz. Then the effect of key parameters on the STL of sandwich structure is systematically analyzed, and the results show that the first frequency of the sandwich shell decreases with the increase of the rib thickness, but increases with the increase of the arc radius. Notably, a smaller arc radius and a larger rib thickness exhibit superior sound insulation properties across a broad frequency range. In addition, when the core layer thickness increases from 0.007m to 0.009m, the average STL of sandwich structures is reduced by 7.38% in a broad low-frequency range of 100–2448Hz.