A Meshless Method For Nonlinear Vibration Of Carbon Fibers Reinforced Composite Plates

Carbon fibers reinforced composite is an advanced composite material with carbon fibers as a reinforcement,which has excellent properties,such as high strength,high modulus and corrosion resistance.It has extremely broad application prospects in aerospace,transportation,infrastructure,sports equipment and other fields.Plate is a main component in the use of composite materials,and usually encounters vibrations caused by large deflection or deformation in their process of using,which has obvious geometric and material nonlinearities,moreover,the spatial distribution of reinforcement is an important influence factor of composite material performances.Therefore,the researches of random spatial distribution of reinforced carbon fibers and nonlinear mechanical behavior and dynamic properties of plates are of important theoretical and practical values.In this paper,the nonlinear vibration characteristics of carbon fibers reinforced composite plate are studied.Firstly,a representative volume element(RVE)model with random distribution of fibers is established,and three statistical descriptors are used to analyze the spatial distribution of fibers.Secondly,a meshless method based on the moving least squares approximation and Galerkin method are employed to study the mechanical properties of transversely loaded carbon fibers reinforced composites.After the model of carbon fibers reinforced composite plates is established,the meshless method is adopted to discretize the system equation and nonlinear vibration equation is obtained.Then,the nonlinear vibration equation is solved via meshless method in an iterative way.Finally,the effects of boundary conditions,aspect ratio,side length and carbon fibers content on the nonlinear characteristics of carbon fibers reinforced composite plates are studied.The research content of this paper can be divided into the following aspects:(1)A new calculation scheme is used to construct a RVE model,and a parameter named as "degree of nonuniformity" is set to control the random distribution of fibers in the matrix.The calculation scheme can generate various fiber spatial distributions according to the known fiber volume fraction,fiber diameter and degree of nonuniformity;three statistical descriptors,namely inter-fiber distance,second order intensity function and radial distribution function,are used to statistically analyze the spatial distribution of fibers.The results show that when the fiber volume fraction is lesser,and the degree of nonuniformity is larger,then the calculation scheme achieve more random distribution of fiber effectively.(2)The equilibrium equations at meso and macro scales are both established,and combining the moving least squares approximation and Galerkin method,the coupled discrete equations are solved,and the mechanical properties of the carbon fibers reinforced composite under lateral load are studied.The damage of the material under a lateral load is analyzed statistically by the radial matrix cracking fraction,and the presented results are compared with experiments and finite element method,and the feasibility and convergence of the proposed multiscale method are verified.Then,the effects of RVE size,influence domain,degree of nonuniformity and fiber volume fraction are discussed,respectively.The conclusion is obtained that when the fiber volume fraction is larger and the degree of nonuniformity is higher,the reinforced fibers can exhibit better performance,meanwhile,the performance of the composite materials is more superior.(3)Combining the classical plate theory and von Kármán large deformation theory,the equilibrium equation of the system including nonlinear term is obtained by the principle of virtual work.The discrete equation is then obtained by meshless method.Firstly,the linear eigenvalues and eigenvectors are determined by solving initial linear equations,and the nonlinear stiffness matrix is calculated by the nondimensionalized amplitude,and then,the nonlinear eigenvalues and eigenvectors are obtained iteratively to analyze nonlinear vibration.(4)The geometrical and material parameters of the carbon fibers reinforced composite plates are selected.Firstly,the feasibility of the nonlinear vibration analysis of carbon fibers reinforced composite via meshless method are investigated;secondly,the effects of various factors,including boundary conditions,aspect ratio,plate length and carbon fiber content,on the nonlinear vibration characteristics of the plates are studied.Finally,it is concluded that the boundary conditions have a great influence on the nonlinear vibration characteristics of plates,and the aspect ratio has a certain influence,while the change of plate length does not affect the nonlinear vibration characteristics.