Forced Vibration Analysis Of FG-GPLRC Plates With Bounded Uncertain Parameters

Functionally gradient graphene reinforced composite(FG-GPLRC)is an advanced composite material.Due to its unique mechanical properties and structural composition,it is used in aerospace,biomedicine,mechanical manufacturing and civil engineering.The field has broad application prospects.However,in actual engineering,uncertainty generally exists,such as processing errors,assembly errors,uncertainties in material properties and uncertain external factors during use,etc.,all have important effects on structural performance,so this article uses In the interval analysis method,the forced vibration of FG-GPLRC plates under lateral impulsive loads under uncertain material physical parameters is studied.The main research contents are as follows:(1)The calculation formula of the pseudo-static sensitivity function has been improved.In general,since the pseudo-static sensitivity function contains items that cannot be directly differentiated,the functions used are simplified functions.In this paper,the finite element perturbation method is introduced to approximate the items that cannot be directly differentiated in the function,in the form of numerical cases The accuracy of the approximate calculation of the finite element perturbation method and the correctness of the complete pseudo-static sensitivity function are verified.(2)The interval method based on pseudo-static sensitivity analysis was used to analyze the influence of the uncertainty of material physical parameters on the dynamic response of FG-GPLRC plates.The interval dynamic response of the FG-GPLRC plates with four GPL distribution modes under the condition that the elastic modulus,density and Poisson’s ratio are uncertain parameters is calculated,and the relative maximum displacements of different GPL distribution modes under the uncertain conditions of each parameter are analyzed in detail And studied the relative maximum displacement with GPL weight fraction and GPL length to thickness ratio.(3)In order to establish the FG-GPLRC interval field method,based on the first-order shear deformation theory,the quadrilateral four-node finite element equation of the FG-GPLRC plate is derived using the Hamiltonian principle and verified by numerical examples The effectiveness of this method.(4)The interval field analysis method based on the finite element method is used to analyze the influence of the interval field with different uncertainty distribution modes on the dynamic performance of FG-GPLRC plates.The spatial average method is used to convert the interval field in each unit to interval value,and then the interval analysis method is used to analyze the influence law of different interval field conditions on the maximum dynamic response of FG-GPLRC plates.