Numerical Investigation of the Vibroacoustic Behavior of Carbon Nanotube Reinforced Doubly-Curved Multilayer Composite Shells

In this paper, a new approach is suggested to analyze the acoustic transmission of carbon nanotube (CNT)-reinforced doubly-curved multilayer composite shells by a three-dimensional (3D) theory, namely the State–Space Method coupled with the fourth-order Runge–Kutta algorithm (SSM-RK4). The properties of nanocomposite media are studied using the principle of mixing rules, which include a number of productivity parameters. Different CNT distributions have been considered, either homogeneous or functionally graded (FG) in the thickness direction. The state equation is firstly established in the sth layer of the considered structure by coupling the behavior law of structure, the equations of deformation and the movement equations according to the State–Space Methodology. The solution of the state equation in the sth layer is taken in the plane wave form, which has enabled us to transform the latter which a partial derivatives equation into a total derivatives equation. For the resolution, the fourth-order Runge–Kutta algorithm (RK4) is used to obtain the propagation matrix in the sth layer. The propagation of the solution in the structure yielded the overall transfer matrix for the structure. Acoustic boundary conditions were applied to obtain the Sound Transmission Loss (STL). Once the STL has been obtained, various representations are presented to check convergence. Not only the accuracy of this method is confirmed, but its importance is as well demonstrated by the reliability of the results obtained, particularly in the high-frequency range. Then, using this method, the effects of different volume fractions, of different CNT distributions, of ratio (radius/thickness), of incident angle and of geometry on the STL were briefly studied. Our results showed that these parameters have decisive and predominant effects on the acoustic insulation performance of CNT composite shells. Variations in these parameters shift the positions of the curvature and coincidence frequencies.