四边简支新型类方形蜂窝夹层结构振动特性研究

新型类方形蜂窝是六边形蜂窝的一种过渡形式，对其等效弹性参数和振动特性的研究具有重要意义。采用改进的Gibson公式对比分析了双壁厚与等壁厚类方形蜂窝夹芯的面内等效弹性参数的差异，并应用经典层合板理论分析了不同等效弹性参数下2种壁厚类型的四边简支类方形蜂窝夹层结构的振动特性，基于有限元仿真技术分析了不同壁厚类方形蜂窝夹层结构的振动特性，并与理论分析结果进行对比。结果表明等效弹性参数的数值模拟结果与理论值基本吻合。在蜂窝基本结构参数相同的条件下，双壁厚类方形蜂窝夹芯的面内等效剪切模量、面外刚度和等效密度均比等壁厚类方形蜂窝夹芯大；在低阶振动模态下，双壁厚类方形蜂窝夹层结构的固有频率比等壁厚类方形蜂窝夹层结构的低，在高阶振动模态下，双壁厚类方形蜂窝夹层结构的固有频率比等壁厚类方形蜂窝夹层结构的高；影响夹层结构固有频率的3个主要因素所占权重由大到小依次为蜂窝夹芯yoz面等效剪切模量、蜂窝夹芯等效密度，蜂窝夹芯壁厚。研究结果表明采用经典层结构理论计算得到类方形蜂窝夹层结构的固有频率与数值仿真结果的一致性较好，这进一步证明了采用改进Gibson公式得到的类方形蜂窝夹芯等效弹性参数的正确性，同时证明了将该振动理论运用到一般蜂窝夹层结构研究的可行性，为扩展研究其他类型蜂窝夹层结构振动特性奠定了基础。

Study on vibration characteristics of new quasi-square honeycomb sandwich structure with all edges simply supported

The new quasi-square honeycomb is one kind of transitional form of hexagonal honeycomb. It is of great significance to study its equivalent elastic parameters and vibration characteristics. The differences of the in-plane equivalent elastic parameters between the quasi-square honeycomb core with the double wall thickness and equal wall thickness were analyzed through the revised Gibson formulas. And the vibration performance of all edges simply supported quasi-square honeycomb sandwich structure with two different wall thickness under the influence of different equivalent elastic parameters was analyzed through the classic laminate theory. A finite element model of the quasi-square honeycomb sandwich structure with different wall thickness was presented to analyze its vibration characteristics, and the simulation results were compared with the theoretical analysis results. The results showed that the numerical simulation results of equivalent elastic parameters were basically in agreement with the theoretical values. Under the same basic structure parameters of the honeycomb, the in-plane equivalent shear modulus, out-plane stiffness and equivalent density of the quasi-square honeycomb core with double wall thickness were larger than those of the quasi-square honeycomb core with equal wall thickness. The natural frequencies of the quasi-square honeycomb sandwich structure with double wall thickness was lower than that of the honeycomb with equal wall thickness in the low-order vibration mode and higher in the high-order vibration mode. The influence of the three main impact factors on the natural frequency of the sandwich structure were listed in descending order as the yoz-plane equivalent shear modulus, the equivalent density and the wall thickness of the quasi-square honeycomb core. Study results indicat that the natural frequency of the quasi-square honeycomb sandwich structure calculated by the classic laminate theory has preferably coherence with the numerical simulation results. The correctness of the equivalent elastic parameters of the quasi-square honeycomb sandwich core obtained by the modified Gibson formula is further proved. This vibration theory is extended to the feasibility of calculating the general honeycomb sandwich structure, which lays a foundation for expanding the vibration characteristics of other types of honeycomb sandwich structures.