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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]

Re-entrant auxetic cellular structures (RACSs) offer various mechanical properties. Specifically, their high acoustic absorption and dissipation properties turn them into proper candidates to effectively increase the sound insulation characteristics of sandwich plates. Accordingly, this approach proposes an analytical strategy to investigate the exact effect of using three-dimensional (3D)-RACS in order to determine the sound transmission loss (STL) coefficient of a sandwich panel. Therefore, the dynamic equations of fluid-structure interaction are extracted using 3D stress distribution, and then the obtained equations are solved analytically based on the state vector method. The reliability and precision of the outcomes are checked according to previous works. The results obtained are significant because the designed sandwich model seems to improve the sound characteristics of the system based on the STL comparisons between the current approach and the single-layer plates as well as sandwich panels with other core geometries. The achievements of this study can provide novel insights into the STL of 3D-RACS sandwich systems with a complex core model. [ABSTRACT FROM AUTHOR]

Vibrational characteristic in structures that can be modeled as several concentrated masses on the beam are of great interest. In this article, variational iteration method (VIM) is used to find a semi-analytical solution for the transverse vibration of an Euler–Bernoulli beam carrying concentrated masses and also to close the condition of the problem into real boundary conditions wherein the cross-sectional changes are applied at points where there is concentrated mass. In order to achieve the Lagrange multiplier, in addition to using variational theory and stationary conditions, a simple polynomial is considered for the initial approximation. [ABSTRACT FROM AUTHOR]

Incremental forming is one of the most well-known forming processes for complex and asymmetric parts. This method uses a CNC machine, simple forming tool, and a die. This study focused on effects of some parameters such as the material, feed rate, pitch, rotational speed and movement strategy of tool on the dimensional precision, forming force, thickness distribution and fracture in the welding area. The results showed that single point incremental forming (SPIF) led to a better thickness distribution with lower tool force, whereas two-point incremental forming led to better dimensional accuracy. Rotational speed does not have any significant impact on the forming process while decreasing the feed rate partially reduced the forming force. According to the results, although dimensional precision in double point incremental forming is better than SPIF, when it comes to the thickness distribution, forming force, and economic issues, SPIF is in favor. The results also showed that by connecting two materials, different parameters for the two materials could be investigated simultaneously in one simulation process. [ABSTRACT FROM AUTHOR]