星型负泊松比蜂窝夹层板的低速冲击动态响应分析  

Dynamic response analysis of star shaped honeycomb sandwich panel with negative Poisson’s ratio under low velocity impact

作　　者：李斌[1] 付涛 LI Bin;FU Tao(School of Mechanical and Electrical Engineering,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学机电工程学院,云南昆明650500

出　　处：《振动工程学报》2024年第11期1925-1935,共11页Journal of Vibration Engineering

基　　金：国家基金青年基金资助项目(52205105);云南省基础研究专项青年项目(202101AU070160)。

摘　　要：将星型负泊松比结构作为夹层板的夹芯层,建立夹层板的动力学模型,推导出夹芯层的等效弹性参数。基于Hertz理论、一阶剪切变形理论和Hamilton原理推导出夹层板的运动方程,应用Navier法对其进行求解。通过两自由度弹簧-质量模型获得冲击接触力,运用Duhamel积分计算出夹层板受小球冲击后的横向位移。与已经发表的论文中对板接触力和横向位移的预测结果进行对比,验证理论分析模型的有效性。同时对比了星型负泊松比夹层板与负泊松比内凹六边形蜂窝夹层板的低速冲击响应,探讨了星型负泊松比蜂窝夹层板的各项参数对冲击性能的影响。结果显示:随着冲击速度的增大,夹层板的最大接触力和最大横向位移增大,冲击响应持续时间缩短;夹层板的厚度比增大,夹层板的冲击性能增强;胞元的边长比减小,夹层板的冲击性能增强;胞元内凹角度增大,夹层板冲击性能提升。本文可为负泊松比超材料结构和夹层板的抗冲击性能研究提供理论参考。The star-shaped negative Poisson’s ratio structure is used as the core of sandwich panels.The dynamic model of a sandwich plate is established,and the equivalent elastic parameters of sandwich layer are derived.The equations of motion of sandwich plates are derived based on Hertz theory,first order shear deformation theory and Hamilton principle.Then,the equations of motion are solved by navier method.The contact force of the impact model is obtained through the spring-mass model with two degrees of freedom,and the lateral displacement of the sandwich plate after impact is calculated by Duhamel integral.The predicted results of plate contact force and lateral displacement are compared with the published papers to verify the accuracy.Meanwhile,the low-velocity impact response of star-shaped negative Poisson’s ratio sandwich panels is also compared with the negative Poisson’s ratio concave hexagonal honeycomb sandwich panels,and the influence of the parameters of sandwich panels is also discussed.When the impact velocity increases,the maximum contact force and the maximum lateral displacement of the sandwich plate also increase,while the duration of the impact response decreases.The greater the thickness ratio of the sandwich plate is,the better the impact performance of the sandwich plate will be.The smaller the side length ratio of cell is,the better the impact performance of sandwich plate will be.The increase of the cell concave angle enhances the impact performance of the sandwich panel.This study can provide some reference for the study of impact resistance of negative Poisson’s ratio metamaterial structures and sandwich panels.

关 键 词：星型负泊松比结构 低速冲击 弹簧-质量模型 动态响应 

分 类 号：TB331[一般工业技术—材料科学与工程] TH142.2[机械工程—机械制造及自动化]