Based on the hyperbolic tangent shear deformation theory, free vibration and sound insulation of two different types of functionally graded (FG) honeycomb sandwich plates with negative Poisson’s ratio are studied in this paper. Using Hamilton’s principle, the vibration and vibro-acoustic coupling dynamic equations for FG honeycomb sandwich plates with simply supported edges are established. By applying the Navier’s method and fluid–solid interface conditions, the derived governing dynamic equations are solved. The natural frequencies and the sound insulation of FG honeycomb sandwich plates obtained in this work are compared with the numerical results by the finite element simulation. It is proven that the theoretical models for the free vibration and the sound insulation are accurate and efficient. Moreover, FG sandwich plates with different honeycomb cores are investigated and compared. The corresponding results show that the FG honeycomb core with negative Poisson’s ratio can yield much lower frequencies. Then, the influences of various geometrical and material parameters on the vibration and sound insulation performance are systematically analyzed.

本文基于双曲切线剪切变形理论，研究了两种不同类型的负泊松比功能梯度（FG）蜂窝夹层板的自由振动和隔声性能。利用Hamilton原理，建立了边缘简支FG蜂窝夹芯板的振动和振声耦合动力学方程。通过应用 Navier 方法和流固界面条件，求解了导出的控制动力学方程。将本文获得的FG蜂窝夹芯板的固有频率和隔声与有限元模拟的数值结果进行了比较。实践证明，所建立的自由振动和隔声理论模型是准确有效的。而且，研究和比较了具有不同蜂窝芯的 FG 夹层板。相应的结果表明，具有负泊松比的 FG 蜂窝芯可以产生低得多的频率。然后，系统地分析了各种几何和材料参数对隔振和隔声性能的影响。