Sound transmission loss analysis of novel sandwich plate with star-shaped auxetic cellular cores

A star-shaped auxetic cellular metamaterial with a negative Poisson’s ratio (NPR) was employed in this study to model lightweight sandwich panels, and an analysis of its sound transmission characteristics was conducted. Utilizing the first-order shear deformation theory (FSDT) and the Hamiltonian principle, the free vibration equation for the sandwich plate is derived. Subsequently, leveraging the fluid-structure coupling condition and incorporating the Navier method, the sound transmission loss (STL) is analytically described. The efficacy of the proposed method is validated through numerical analysis and an acoustic insulation experiment using an impedance tube. Based on the theoretical modeling, it is calculated that the sound insulation effect of the star-shaped cellular core exceeds that of the traditional reentrant cellular with NPR. A systematic analysis is subsequently conducted to explore the impact of star-shaped cellular structure parameters on the STL of the sandwich panel. It can be obtained that the increase in core layer thickness leads to a reduction in the first-order resonance frequency of the sandwich panel, but concurrently diminishing its sound insulation performance. The change of the connecting rib length exerts a more considerable influence on the structure’s STL compared to the side rib length. While as the cell wall thickness reduces from 2.0 to 1.0 mm, the average STL of the sandwich plate across the analysis band decreases by 8.43%, from 46.3 to 42.7 dB.