曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性，可以在大变形过程中吸收能量、抗冲击，并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层，建立夹层板的动力学模型；推导出了曲壁负刚度蜂窝胞元的等效弹性参数，将其周期性排列为蜂窝芯，应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程；应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型，计算固有频率，与理论计算结果进行比较，结果显示二者的计算结果具有较好的一致性，验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下，夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。

Study on vibration characteristics of curved wall honeycomb sandwich plates

The curved-wall honeycombs have negative stiffness characteristics, which can absorb energy and isolate shocks during large deformations. They can recover themselves instead of being crushed like the traditional honeycombs after the impact loads. In this paper, the curved-wall negative stiffness honeycombs are used as the core layer and then the dynamic model of the sandwich plate is established. The equivalent elastic parameters of the curved-wall honeycomb cells are deduced including the Young's modulus, Poisson's ratio and the shear modulus. Afterwards the negative stiffness honeycomb cells are arranged periodically as the core layer of the sandwich plate. By using the Reddy’s higher-order shear deformation theory, Von-Karman large deformation relationship and Hamilton principle, the nonlinear dynamical equations of the honeycomb sandwich plate are derived. The Navier method is used to calculate the natural frequencies of the plate under the boundary conditions of simply supported on four sides. Simultaneously, the finite element model of the sandwich plate is established by the solid units, and the natural frequencies are derived by using ABAQUS software. The results show that the natural frequencies from the two methods are in good consistency, which verify the validity of the equivalent elastic parameters of the curved wall honeycomb layer. Finally, the variation characteristics of natural frequencies of the sandwich plate with different core thickness, different core thickness ratio and different curved-wall thickness are discussed when the energy absorption capacity of the honeycomb cells is better. The results obtained in this paper will provide a basis for further research on the dynamics of negative stiffness honeycomb plates and will give certain guidance for the applications of negative stiffness honeycombs to sandwich structures and vibration isolation mechanisms.