Bending And Vibration Analysis Of Micro-carbon Nanotube-reinforced Composite Plates

The free vibration and static model of orthotropic functionally graded carbon nanotubes reinforced composite plate is developed based on a new modified couple stress theory.The present model can describe the scale effects with only one material length parameter incorporated.Hence,it is extremely convenient for engineering application.The motion equations and governing equations and related boundary conditions are derived based on the Hamilton's principle in conjunction with the third-order shear deformation theory.A simply supported square plate is taken as illustrative example and analytical solved.The effect of the plate thickness,volume fraction and distribution of carbon nanotubes on the natural frequencies of the plate is investigated.Numerical results indicate that the natural frequencies predicted by present model are always higher than those by classical theory.The difference between the natural frequencies predicted by the two models is significant when the plate thickness is approach to the material length parameter,but is diminishing with the increase of the plate thickness.The further study shows that,with the increase of the volume fraction of carbon naotubes,the center deflections decrease and the frequencies increase.It is show that carbon nanotubes can improve the stiffness of the structure.In addition,the distributions of carbon nanotubes has remarkable effect on the deflection plate center and frequencies.