负泊松比蜂窝夹层板的振动特性研究  

Vibration analysis of honeycomb sandwich plate with negative Poisson's ratio

作　　者：朱秀芳 张君华 

机构地区：[1]北京信息科技大学机电工程学院,北京100192

出　　处：《应用力学学报》2018年第2期309-315,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11472057);北京信息科技大学"勤信人才"培育计划(QXTCPB201701);深圳市科技计划项目(JCYJ20160608153749600);机电系统测控北京市重点实验室开放课题(KF20171123202)

摘　　要：研究了负泊松比蜂窝夹层板几何参数变化对板振动频率的影响,并得到了频率随泊松比的变化规律。在Reddy高阶剪切变形理论的基础上,利用Hamilton原理,推导出四边简支边界条件下的负泊松比蜂窝夹层板的偏微分运动方程。根据修正后的Gibson公式,考虑了蜂窝胞元壁板的弯曲和伸缩变形,重新计算了蜂窝芯层胞元的等效弹性参数。利用Navier法,选择合适四边简支边界条件的模态函数,得出板的长厚比分别为0.01、0.05、0.10,芯厚比分别为0.80、0.85、0.90、0.95和蜂窝芯胞元倾角分别为-30°、-60°、0°、30°、60°等情况下系统的前五阶固有频率。研究结果表明,系统的固有频率随板的芯厚比、蜂窝芯胞元倾角、蜂窝芯壁厚与斜壁之比的增加都在减小,而随着板长厚比的增加而增加。分析了泊松比的变化对系统固有频率的影响,发现负泊松比蜂窝夹层板的固有频率要明显小于传统正泊松比蜂窝夹层板。本文所得结果对进一步研究系统的多模态共振具有指导意义,为负泊松比蜂窝夹层结构的工程应用在减振设计方面提供一定的理论依据。Influence of geometric parameters of an auxetic honeycomb sandwich plate on the vibration frequencies of the plate is studied and the variation law of the frequencies with Poisson's ratios is obtained. The nonlinear governing equations of motion for the negative Poisson's ratio honeycomb sandwich plate are derived by using the Reddy's higher-order shear deformation theory and the Hamilton's principle. According to the modified Gibson formula, the equivalent elastic parameters of the honeycomb cores are recalculated considering the bending and axial compression and deformation of the honeycomb cells. The Navier method is used to select the modal function suitable for the simply supported boundary conditions, and the first five natural frequencies of the system are obtained under the length-thickness ratios are 0.01、0.05、0.10, the core thickness ratios are 0.80、0.85、0.90、0.95, the cell angels of the honeycomb core are-30°、-60°、0°、30°、60°, respectively. Influence of Poisson's ratio on the natural frequency of the system is analyzed. It is obtained that the natural frequencies of negative Poisson's ratio honeycomb sandwich plate are significantly smaller than the traditional positive Poisson's ratio honeycomb sandwich plate. Results obtained in this paper are of significance to further study the multimodal resonance of the system and theoretical basis for vibration design of negative Poisson's ratio honeycomb sandwich structures.

关 键 词：负泊松比 蜂窝夹层板 固有频率 自由振动 

分 类 号：TB33[一般工业技术—材料科学与工程]