碳纳米管增强复合材料是一种既满足航空航天、医学生物等高技术领域的需要，又满足在极限环境下反复正常工作的新型功能材料。研究了压电碳纳米管增强复合材料（functional gradient carbon nanotube reinforced composites, FG-CNTRC）夹层板的自由振动和隔声特性，考虑了两种不同的芯层分布形式，即对称的FG-X型分布和非对称的FG-V型分布。基于三阶剪切变形理论，建立了四边简支边界条件下的动力学方程和声振耦合方程，利用纳维法和流固耦合条件，求解得到结构振动固有频率和隔声量。通过有限元模拟，验证了理论模型的正确性和可行性，在此基础上，讨论了参数变化对自由振动和隔声特性的影响，研究结果为夹层板在工程上的应用提供了理论基础。

Carbon nanotube reinforced composites are a new type of functional material that meets the needs of high technology fields such as aerospace and medical biology, as well as repeated normal operation in extreme environments. The free vibration and sound insulation characteristics of piezoelectric carbon nanotube reinforced composite (functional gradient carbon nanotube reinforced composites, FG-CNTRC) sandwich plates were studied, which consider a symmetric FG-X distribution and an asymetric FG-V distribution. Based on the third-order shear deformation theory, the dynamic equation and vibro-acoustic equation under four simply supported boundary conditions were established. By using the Navier method and fluid-solid coupling conditions, the natural frequency and the sound insulation were obtained. The correctness and feasibility of the theoretical model were verified through finite element simulation. Then, the influence of parameter changes on free vibration and sound insulation characteristics was discussed. This research provides a theoretical basis for the application of sandwich plates in engineering.