An analysis of broadband low-frequency sound insulation in porous functionally graded sandwich panel with vertical strut combined re-entrant auxetic cellular core

Cellular structures exhibiting negative Poisson's ratio (NPR) effects are highly promising for lightweight sandwich structures owing to their outstanding mechanical properties. This study investigates the broadband low-frequency sound transmission loss (STL) characteristics of a novel sandwich panel configuration that integrates porous functionally graded material (PFGM) face sheets with a vertical strut combined re-entrant (VSCR) auxetic cellular core. Material gradation followed both power-law and exponential distributions, while four distinct pore distribution patterns (Types A-D) were examined. The proposed sandwich structure was analytically modeled using first-order shear deformation theory (FSDT) and the Hamiltonian principle, with fluid-structure interaction at the interfaces solved via Navier's method. Theoretical predictions were validated against published results, experimental data, and simulation outcomes, showing good agreement. Comparative analyses revealed that the VSCR auxetic core significantly outperforms conventional re-entrant designs in STL performance. Among the configurations studied, the power-law gradient distribution combined with Type-B pore arrangement yielded optimal acoustic insulation, within the 100-2448 Hz low-frequency range, the B-type pattern providing an 11.33% higher average STL than the uniform Type-A distribution. Furthermore, the influence of various structural parameters of the cellular core, including the re-entrant angle, horizontal arm length, cell wall thickness, and re-entrant arm length, on the STL of the sandwich plate was systematically analyzed. These findings offer valuable guidance for designing lightweight, high-performance sound-insulating sandwich structures.