| Graphene nanoplatelets(GPLs)is considered to be the strongest material to date,with tensile strength and elastic modulus reaching 130 GPa and 1 TPa respectively.It is also abundant in nature,and it is the most promising ultra-lightweight reinforcement material in composite materials.Functionally graded material(FGM)is a new kind of inhomogeneous composite material,its material properties can be continuous gradient along the direction of one or more changes.In recent years,GPLs has been introduced into function graded composites,it has been deeply studied by scholars all over the world.However,due to the limitation of the current manufacturing technology,there are many uncertainties in the practical application of the composite material,and the influence of these uncertainties on the dynamic performance of the structure is not clear.In this paper,the interval,interval field and random-interval analysis methods are established under the condition of uncertain material parameters,and the influence of uncertainty of key parameters on FG-GPLRC plate free vibration performance is studied by numerical simulation.The main research content and results are as follows:(1)Based on the first-order shear deformation plate theory,the vibration control equation of FG-GPLRC plate is obtained according to the Hamiltonian principle,and the eigenvalue equation of FG-GPLRC plate is obtained according to the Navier method based on the boundary conditions.Based on sensitivity analysis and interval arithmetic theory,aformula for calculating the upper and lower bound of the natural frequency interval is established.The elastic modulus,mass density,poisson's ratio of each layer of laminated plates,as well as the structural appearance size,are considered as interval uncertainty variables.The numerical results show that the uncertainty of frequency mainly depends on the appearance size of the structure,the density and the Young's modulus of the material,while the influence of Poisson's ratio can be almost ignored.Comparing with the polymer matrix,the parameters of graphene affect the natural frequency more significantly.(2)The finite element method for analyzing the free vibration of the FG-GPLRC plate was established according to the quadrilateral four-node isoparametric element.Further,considering the spatial distribution uncertainty of GPLs,the weight ratio of GPLs was modeled as an interval field uncertainty variable.The results show that the incorporation of GPLs has the greatest influence on the stiffness and frequency of the structure.In the plane coordinates,the distribution of GPLs on the surrounding boundary is better than the centralized distribution in the center,which can improve the stiffness of the structure.In terms of interlayer coordinates,dispersing more GPLs near the top and bottom surfaces of plate can improve the reinforcement efficiency but increase the sensitivity of natural frequency to parameters of materials.(3)Finally,the expressions for the mean value and variance of natural frequencies are derived by using a hybrid stochastic and interval approach.The bounds of these probabilistic Characteristics are then determined by interval arithmetic.Then,the elastic modulus and mass density of GPLs and polymer matrix were modeled as mixed random and interval parameters.The numerical results show that more material parameters are assumed as interval and random parameters,the uncertainty of frequency will tend to be higher.The uncertainty of the obtained structure frequency mean value has a linear superposition relation with the change of different interval-random combinations.However,the standard deviation of frequency is not a simple linear superposition of the results of physical parameters of random materials.The method and conclusion of this study will be helpful to the development of FG-GPLRC structure analysis theory and engineering application method. |
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