Quasi-static and sound insulation performance of a multifunctional cylindrical cellular shell with bidirectional negative-stiffness metamaterial cores

Abstract

This paper presents a novel type of cylindrical cellular shell with bidirectional negative stiffness (NS) metamaterial cores. The unit cell is composed of a trapezoidal frame and four cosine-shaped curved walls, therefore showing NS effect in both the circumferential and radial directions. Numerical analyses are conducted to investigate the mechanical properties, including the quasi-static behavior under radial compression and the sound transmission loss (STL) performance under an outward radiation wave within a wide frequency range. The acoustic performance is compared with those of cylindrical shells with annular hexagonal and re-entrant honeycomb cores. The NS-core and honeycomb-core cylindrical cellular shells are with the same outline dimensions and overall weight. Parametric studies of the STL on the thicknesses of the curved cell walls and the weight of mass inclusions are performed, followed by optimizations with the purpose of maximal averaged STL in two specified frequency ranges. It was found that the NS-core cylindrical shell yielded much higher STL than those honeycomb-core cylindrical shells for frequencies larger than about 200 Hz. Furthermore, the averaged STLs of the optimized designs increased by 123.7% and 39.5% for the two ranges, respectively. The results indicate that the proposed shell is not only able to endure large strain due to elastic instability, but also isolates sound waves under the very small sound-induced deformation. This design provides an alternative to the conventional core types in cellular structures by showing abundant designability and desirable structural and vibro-acoustic characteristics.