Dynamic Analysis Of Axially Moving Graphene Reinforced Laminated Composite Plate

Since the advent of graphene,it has attracted the attention and research of many scholars because of its excellent mechanical properties.The nanocomposites with excellent performance can be obtained by adding graphene nanoplatelets(GPLs)as reinforced phase to the matrix.Axially moving structures have been widely used in engineering,such as cutting chainsaw,power transmission belt,and spacecraft solar panel.In this work,GPLs are added to the axially moving plate and the dynamic characteristics of graphene reinforced axially moving laminated composite plate are investigated.The main research contents are as follows:(1)The dynamic modeling of graphene reinforced axially moving laminated composite plate is carried out.The displacement field is determined according to the classical plate theory,and the von Kármán large deformation theory is adopted in the geometric relation.The constitutive relation of the plate considering piezoelectric effect and temperature change are given.The dynamic equations of the axially moving plate is obtained by using Hamilton's principle.Considering the simply supported–simply supported and fixed–free boundary conditions,the modal functions of structural vibration are determined,respectively.The Galerkin method is utilized to discretize the dimensionless nonlinear dynamic partial differential equations in the form of generalized displacement,and the two-degree-offreedom ordinary differential equations of the axially moving plates under simply supported–simply supported and fixed–free boundary conditions are obtained,respectively.(2)The dynamic characteristics of the axially moving laminated plate with simply supported boundary condition are studied.In the case of axially moving simply supported plate with constant velocity,the stability analysis is carried out through the complex eigenvalues of linear part coefficient matrix of ordinary differential equations,focusing on the critical and flutter velocities of the system.In the case of axially moving simply supported plate with varied velocity,the instability region boundary of combination and subharmonic resonances for the parametric excited vibration of the linear part of the timevarying system is analyzed via direct multi scale method.For the nonlinear system,the subharmonic resonance is considered,the multi scale method is utilized to analyze the system,and the amplitude-frequency relation and stability condition are obtained.The effects of parameters such as GPL total volume fraction,distribution pattern,length-tothickness and length-to-width ratios,electric field voltage,graphene piezoelectric coefficient,and temperature on the dynamic characteristics of the axially plate with simply supported boundary condition are analyzed.(3)The dynamic characteristics of axially moving laminated plate with cantilever boundary condition are studied.Considering the case of cantilever extending plate with constant velocity,the stability of the system is determined according to the eigenvalues of coefficient matrix of ordinary differential equations,and the critical velocities of the cantilever plate with instantaneous fixed length and variable length during extension process are carried out,respectively.The time history relation of the cantilever plate during extension is simulated via the Runge-Kutta method,and the time-varying dynamic characteristics of the plate during extension are analyzed.The effects of GPL distribution and dimension,piezoelectric effect,and temperature change on the time-varying dynamic characteristics of graphene reinforced axially moving cantilever laminated composite plate are studied.