多孔石墨烯增强复合材料截锥壳的动力稳定性

Dynamic Stability of Porous Truncated Conical ShellsReinforced with Graphene Platelets

为研究弹性介质中含孔隙的石墨烯增强复合材料截锥壳的动力稳定性,基于Halpin-Tsai微观力学模型和经典薄壳理论建立了截锥壳动力稳定的控制方程,并用Bolotin法分析了临界激励频率和动力稳定区域.研究结果显示,在3种孔隙分布中,孔隙集中于中部分布的临界激励频率最大.在5种石墨烯分布中,非线性集中于中部的临界激励频率最大.当石墨烯含量从0.1%增大到0.9%时,临界激励频率约增大97%.在10°、30°、50°和70°四种半锥角中,30°的临界激励频率和非稳定区域最大.与压缩刚度相比,弹性介质的剪切刚度对临界激励频率和稳定区域的影响更大.可见优化设计石墨烯的含量和分布模式,可提高石墨烯增强复合材料截锥壳的动力稳定性.

Based on Halpin-Tsai micromechanical model and classic shell theory,the goverming equations o motion were derived to study the dynamic stability of porous funct ioally graded truncated conical shells reinforced by graphene platelets(FG-GPLs).The Bolotin method was employed to obtain the critical excitation fre-quencies and unstable regions.The results show that the critical exci tation frequency,more pores distributed in the middle,is higher than those for the other two types of pore distribution.Among the five patterns of GPLs distribution,the critical excitation frequency,nonlinear distributed in the middle,is the largest.As the mass fraction of GPLs rises from0.1%to0.9%,the critical excitation frequency is increased by about 97%。Among the four semivertex angles of 10°,30°,50°and 70°,the critical excitation frequency and unstable regions for 30°are the largest.Compared with the compressive siffness of the elastic media,the shear stiffness has more significant efcts on the critical excitation frequency and stable region.Hence,the dynamic stability of FG-GPLs truncated conical shells can be improved by optimizing the design of the content and distribution of GPLs.