直曲增强型负泊松比超材料的力学性能与减振研究

负泊松比超材料结构作为一种新型智能材料与结构,精确计算超材料结构在大应变下的非线性力学性能对其在工程中的潜在应用具有重要意义.本文在弧形内凹负泊松比结构中加入直杆,设计了一类直杆增强型直曲耦合内凹超材料结构；利用能量法推导出了曲边内凹蜂窝结构的横/纵向等效泊松比与等效弹性模量的解析表达式,讨论结构各参数对结构等效泊松比与等效弹性模量的影响.考虑几何非线性大变形,建立了曲边内凹负泊松比结构的有限元模型,并与线性模拟结果对比,验证了解析表达式的正确性.结果表明,等效泊松比与等效弹性模量均随变形增大而变化,且变形越大差异越明显,大变形下须考虑几何非线性；利用谐响应分析计算结构的加速度级和加速度振级落差,凸显所设计超材料结构的减振性能；分析结构整体减振性能,发现其随层数增加逐渐增大；不随频率变化,在低频范围内对激励产生的响应能够起到抑制作用.因此,合理的设计超材料微结构对结构的低频振动具有很好的抑制作用,对负泊松比超材料减振结构设计具有一定的参考意义.

Mechanical Properties and Vibration Reduction Analysis of a Straight-Arc Strut Enhanced Metamaterials with Negative Poisson's Ratio

As a new type of smart materials and structures, the accurate prediction of the nonlinear mechanical properties of metamaterial structures with negative Poisson''s ratio under large strains is of great significance for their potential applications in engineering. In this paper, a class of metamaterial structures enhanced by straight struts are designed by adding straight struts to ratio arc-shaped structures with negative Poisson''s ratio. The analytical expressions of the transverse/longitudinal equivalent Poisson''s ratio and equivalent elastic modulus of the concave honeycomb structure are derived by energy method. The effects of structural parameters on the equivalent Poisson''s ratio and equivalent elastic modulus of the structure are discussed. Considering the geometric nonlinearity under large deformation, a finite element model of re-entrant arc-shape structure with negative Poisson''s ratio is established. The correctness of the analytical expression is verified by comparing with the linear simulation results. The results show that the equivalent Poisson''s ratio and equivalent elastic modulus both varies with the increase of deformation. The differences increase with the increased deformation. Therefore, geometric nonlinearity analysis must be considered in the case of large deformation. The vibration reduction performance of the designed metamaterial structure is calculated by using the harmonic response analysis. The analysis shows that the overall damping performance of the structure increases gradually with the increase of the number of layers. The overall vibration reduction performance of the structure does not change with the frequency, and the response to excitation can play a very good inhibitory effect in the low frequency range. Therefore, the rational design of metamaterial microstructure has a good effect on the low frequency vibration suppression of structures, and has a certain reference significance for the design of vibration reduction metamaterial with negative Poisson''s ratio.