Broadband low-frequency sound insulation of stiffened sandwich PFGM doubly-curved shells with positive, negative and zero Poisson's ratio cellular cores

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative and zero Poisson's ratios have unique mechanical deformation characteristics, which can be further applied to modeling lightweight sandwich structures. Based on that, the sound transmission characteristics of a novel stiffened sandwich porous functionally graded materials (PFGM) doubly-curved shells with full Poisson's ratio characteristic range cellular cores are investigated in this study. The adjustment of material properties of PFGM face sheets in the thickness direction is achieved through power law based on component volume fraction, and the core layer consists of cellular cores with positive, negative, and zero Poisson's ratios (PPR, NPR, and ZPR). Two common types of stiffened sandwich shell types, namely, the shell with PFGM face sheets and metal-rich cellular cores (type-A), and the ceramic-rich cellular cores (type-B), are discussed, and the Hamilton's principle is used to derive the governing equations. By applying normal velocities continuity conditions at the fluid-structure interface to consider fluid-structure coupling, which is further analytically solved using Navier's technology, and the average sound transmission loss (STL) with broadband low-frequency is described. The effectiveness of the established theoretical model is confirmed by comparing it with previously published results, experimental and simulated results obtained by impedance tube and COMSOL commercial software. A systematic comparison is conducted on the performance of stiffened sandwich PFGM doubly-curved shells with full Poisson's ratio characteristic range cellular cores, and the results show superior performance in the sound insulation for the sandwich shell with ZPR cellular cores, considerably at a broad low-frequency range of 220–2040 Hz, in comparison with the sandwich shell with NPR cellular cores and conventional PPR cellular cores types. This work's findings can serve as a benchmark for future studies and help to design and create engineering sandwich structures with improved sound insulation properties.