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Sound transmission loss (STL) can be augmented in buildings using graphene nanoplatelets (GPLs) and metamaterials. The present study established an analytical model grounded on the three-dimensional (3D) elasticity theory to predict STL in a doubly curved shell with a 3D re-entrant auxetic cellular core (3D-RACS) and GPLs as the top layer. The state space method was used to offer an analytical solution, where each part of the structure was divided into a number of layers and each layer into several sublayers. The stiffness matrix of the core was developed according to elastic properties such as Young's modulus, shear modulus, and Poisson's ratio out of the plane. The findings revealed that GPLs as the top layer had a tremendous impact on the structure's performance. Furthermore, the effects of 3D-RACS and GPL parameters on the structure's STL were investigated in the stiffness and mass control domains. Accordingly, the addition of the core material significantly affected high frequencies, particularly in the mass control domain. Finally, the results indicated that curvature and coincidence frequencies could be changed by optimizing 3D-RACS and GPL parameters. Doubly curved structures have different applications in different industries, and due to the complexity of their modelling, they have been used less in research. Nowadays, structural vulnerability to acoustic waves is a concern in the industry, and designers seek to prevent the transmission of acoustic waves into the structure. This is why the study of sound transmission loss is so broad. One of the best methods is to increase the rigidity of the structure because increasing the stiffness of the structure increases the sound transmission loss. In this regard, auxetic materials (3D-RACS) used as a type of metamaterial can have a significant impact on increasing the loss of sound transmission. Due to the use of a sandwich structure in this research, however, GPL material is used for the outer wall exposed to waves. This material can increase the structural rigidity of a structure despite its lightness. Finally, by designing such a structure and comparing the results, a very effective output has been obtained. [ABSTRACT FROM AUTHOR]