Vibro-acoustic performance and design of annular cellular structures with graded auxetic mechanical metamaterials

Abstract

An exciting paradigm in the ongoing development of materials is the development of auxetic mechanical metamaterials, which can be flexibly designed to exhibit a unique range of physical and mechanical properties. Inspired by nonuniform or nonhomogeneous metamaterials and structures, annular cellular structures composed of auxetic metamaterials with graded negative Poisson's ratios (NPRs) are studied, and the considered models are divided into two types of configurations: models with graded decreasing NPRs and models with graded increasing NPRs along the radial direction. The spectral element method (SEM) is applied to accurately predict the structural dynamic responses with a limited number of elements and the system scale for arbitrary frequencies. The static stiffness and vibro-acoustic performance of the proposed structures are investigated and compared. The computational results show that the bending stiffness, vibrating mode shapes and deformations, and sound transmission loss (STL) of the considered cellular structures are strongly affected by the arbitrarily patterned graded auxetic metamaterials. Within the studied STL frequency range from 1 to 1500 Hz, optimal designs of the conventional and graded configurations for the maximum STL are obtained for specified tonal and frequency band cases under cylindrical incident sound waves. The results show that the graded configurations have more potential than the conventional ones for optimal acoustic performance and that compared with the graded decreasing NPR models, the graded increasing NPR models exhibit STL increases of 6.73 dB, 1.22 dB, and 2.06 dB for the studied cases. Both the STL and optimal design results indicate the advantages of the graded increasing NPR models for use in acoustic attenuation applications. Thus, graded auxetic metamaterials offer a great opportunity for achieving unusual vibro-acoustic performance and extending the route to obtain an optimized set of physical properties for cellular metamaterials and structures.