Acoustic sound propagation of a doubly curved shell with 3D re-entrant auxetic cellular metamaterials

The primary purpose of this study is to investigate the sound transmission loss (STL) on a doubly curved shell with the three-dimensional re-entrant auxetic cellular structure (3D-RACS). First, the modeling of doubly curved shells is solved by applying 3D elasticity theory using the state space method. In addition, the elastic properties of 3D-RACS are obtained out of the plane. Then, STL can be obtained by applying the boundary conditions. The validation of this problem is checked compared to other studies, which indicates an excellent agreement. In addition, the effects of core parameters on STL are determined. Accordingly, embedding the core's crucial substantial effect reduces the amount of curvature frequency. The control domain has no main effect on other parts of the stiffness. However, in the mass control domain, adding the core into the structure significantly affects the increase of STL and will change the value of coincidence frequency.