以一阶剪切变形理论为基础，利用Hamilton原理得到阻尼板的振动平衡方程。采用Navier闭环型解对四边简支约束的阻尼板结构进行求解，与仿真结果进行对比验证，证明所推导振动平衡方程的正确性，使用验证过的方程对结构动态特性进行分析。结果表明：当将特定的阻尼材料合理嵌入复合材料板的厚度达到一定值时，整体复合材料阻尼板结构的前四阶振动频率最小且损耗因子最大；保持复合材料层厚度不变，改变嵌入的阻尼材料的厚度和边长，振动频率逐渐减小，结构的损耗因子逐渐增大。

Based on the first-order shear deformation theory, the vibration balance equation of damping plate was obtained by the Hamilton principle. The Navier closed-loop solution was used to solve the damping plate structure with four sides simply supported constraints, and the correctness of the deduced vibration balance equation was verified by comparison with the simulation results. The verified equation was used to analyze the dynamic characteristics of the structure. The results show that the vibration frequency of the first four orders of the composite damping plate structure was the smallest and the loss factor is the largest when the thickness of the composite sandwich plate with a specific damping material was inserted to a certain value. When the thickness of the composite layer was kept constant and the thickness and side length of the embedded damping material were changed, the vibration frequency decreased and the loss factor of the structure increased.