石墨烯三相复合材料板的非线性动力学研究

研究带有石墨烯涂层的1-3型压电纤维复合材料(MFC-GP)简支板结构的非线性动力学特性.首先,基于Reddy一阶剪切变形理论、Von Kármán位移应变关系以及Hamilton原理,推导了MFC-GP复合材料板的非线性偏微分方程.根据边界条件选择适当的模态函数,利用Galerkin法将偏微分方程离散成两自由度的常微分方程.采用多尺度方法进行摄动分析,得到结构在1∶1内共振下的频响方程,分析了石墨烯体积分数、电压、温度等对结构非线性频响曲线的影响.通过数值模拟,运用分叉图、相图、波形图研究了外激励对MFC-GP板非线性振动响应的影响.结果表明:不同参数及外激励下,结构出现了复杂的非线性动力学行为,对今后的工程实际应用具有一定的指导意义.

Nonlinear dynamics of a three-phase composite materials plate with graphene

In this paper,the nonlinear dynamic characteristics of simple supported plate structures of 1 3 type piezoelectric fiber composites (MFC GP) coated with graphene were studied. First,the nonlinear partial differential equation of the MFC GP composite material plate was deduced based on the Reddy first order shear deformation theory,Von Kármán displacement strain relation and Hamilton principle. Then,it was discretized into two degree of freedom ordinary differential equation by the Galerkin method. Furthermore,the frequency response equation with internal resonance 1:1 was obtained by the multi scale method,and the effects of volume fraction of graphene,voltage,temperature and initial phase on the frequency response curve were analyzed. Finally,the vibration response of MFC GP composite plate was investigated by using bifurcation diagram,phase diagram and waveform through numerical simulations. The results were shown complex nonlinear vibrations of the plate with different parameters and external excitations,which would have certain guiding significance for future engineering application.