功能梯度多层石墨烯增强纳米复合材料圆弧拱的参数失稳分析

针对功能梯度多层石墨烯增强纳米复合材料(functionally graded multilayer graphene nanoplatelets reinforced composite,FG-GPLRC)圆弧拱的参数失稳问题,基于Halpin-Tsai的复合材料微观力学模型和有限单元法理论建立了FG-GPLRC圆弧拱在拱顶作用周期荷载的运动控制方程,并转化为含阻尼项的Mathieu-Hill方程。利用Bolotin方法求解Mathieu-Hill方程获得FG-GPLRC圆弧拱的主动力不稳定区域,并分别研究了石墨烯纳米片(graphene nanoplatelets,GPLs)的分布类型、质量分数、几何形状对FG-GPLRC圆弧拱动力不稳定性的影响。数值结果表明,GPLs沿拱截面厚度方向的顶层和底层分布较多时能够明显减小FG-GPLRC圆弧拱的面内不稳定区域,提高其结构稳定性。当GPL的高宽比大于4和宽厚比大于103时,GPL的几何形状对FG-GPLRC圆弧拱的动力稳定性影响不再明显,且随着结构阻尼系数的增大,FG-GPLRC圆弧拱发生参数失稳的临界荷载也增大,从而降低了结构发生动力失稳的概率。

PARAMETERS INSTABILITY OF FUNCTIONALLY GRADED MULTILAYERGRAPHENE NANOCOMPOSITE CIRCULAR ARCHES

The parameters instability of functionally graded multilayer graphene nanocomposite (FG-GPLRC) circular arches is studied and the effective material properties of GPLRCs is estimated by Halpin-Tsai micromechanics model. The governing equations of motion for the FG-GPLRC arch under a periodic load is derived by the finite element method, which is converted to a linear damping system of Mathieu-Hill equation. The Mathieu-Hill equation is solved by Bolotin method to obtain the principle unstable region of FG-GPLRC arches and the special attention is given to the effect of GPL distribution pattern, weight fraction, geometry and dimension on the dynamic instability behavior. Numerical results show that distributing more GPLs to the top and bottom along the thickness direction can effectively reduce the size of the unstable region and improve the stability of the FG-GPLRC arch. The influences of GPL geometry and dimension tend to be insignificant when the aspect ratio and flakiness ratio of GPLs are greater than 4 and 103 respectively, and the critical load causing parameter instability for the FG-GPLRC arch increase as the damping coefficient increase, which also reduce the probability for parameter instability of the FG-GPLRC arch.