弹性地基上多孔功能梯度复合材料纳米圆柱壳的自由振动研究  

Study on Free Vibration of Porous Functionally Graded Composite Materials Cylindrical Nanoshell Resting on Elastic Foundation

作　　者：张飞[1] 白春玉[1] Zhang Fei;Bai Chunyu(Aviation Key Laboratory of Science and Technology on Structures Impact Dynamics,Aircraft Strength Research Institute of China,Xi'an 710065,China)

机构地区：[1]中国飞机强度研究所结构冲击动力学航空科技重点实验室,陕西西安710065

出　　处：《航空科学技术》2021年第8期49-56,共8页Aeronautical Science & Technology

摘　　要：为了体现弹性地基对功能梯度材料(functionally graded materials, FGMs)纳米圆柱壳力学特性的影响并考虑到FGMs结构中可能存在的孔隙,基于Mindlin应变梯度理论,建立了弹性地基上包含尺寸效应的多孔FGMs一阶剪切变形纳米壳的力学模型,这种非经典的连续介质力学纳米壳模型利用材料长度尺度参数捕捉尺寸效应。通过Hamilton变分原理得到了系统的运动微分方程,采用Navier法获得了FGMs纳米壳固有频率的解析解,研究了Winkler弹性地基上多孔FGMs纳米壳的自由振动特性。结果表明,FGMs纳米壳孔隙率的增加会导致固有频率显著降低;Winkler弹性地基增加了FGMs纳米壳的有效刚度,且纳米壳的固有频率随着Winkler弹性常数的增加而增加;随着无量纲材料长度尺度参数的增加,基于非经典连续介质力学模型得到的纳米壳固有频率逐渐收敛于基于经典模型得到的结果。提出的建模方法可以为纳米圆柱壳的相关科学研究提供借鉴和参考;研究结果可以为相关工程设计提供依据。In order to reflect the influence of elastic foundation on the mechanical properties of functionally graded materials(FGMs) nanoshells and considering the porosities in the FGMs structure, the porous FGMs first-order shear deformation nanoshells resting on the Winkler elastic foundation is established by using Mindlin’s strain gradient theory. The material length scale parameter is used to capture the size effect of the FGMs nanoshells. The differential equations of motion of the system are obtained via Hamilton’s variational principle. The natural frequencies of the FGMs nanoshells are obtained by using the Navier method. And then, the free vibration of the porous FGMs nanoshells resting on the Winkler elastic foundation was studied. The results show that an increase in the porosity coefficient of the FGMs nanoshells results in a lower natural frequency. Winkler elastic foundation increases the effective stiffness of the FGMs nanoshells, and the natural frequencies of nanoshells will increase with the increase of the constant of the Winkler elastic foundation. With the increase of the dimensionless material length scale parameter,the natural frequencies obtained by the non-classical continuum theories converge to the results based on the CT model. The proposed modeling method can provide reference for the related scientific research of nanoshells, and the research results can provide a basis for related engineering design.

关 键 词：应变梯度理论 功能梯度复合材料 弹性地基 自由振动 孔隙率 

分 类 号：V214.4[航空宇航科学与技术—航空宇航推进理论与工程]