Vibration,Buckling And Dynamic Stability Of Axially Moving Functionally Graded Plates

Axially moving plates are widely used in traffic,machinery,aerospace and other fields.In order to design a reasonable motion velocity and improve the working efficiency of the plate,we must understand the effects of its material characteristics,axial velocity,etc.on the buckling,vibration and dynamic stability of the plate.In this paper,the effects of different parameters on buckling,vibration and dynamic stability of axially moving plates are studied with the example of(FGM)plates,which are light in weight,high in strength and good in resistance to moisture and heat.It provides a very important theoretical significance and application value for further popularizing the application of functionally graded materials in traffic engineering structures.The main contents of this article are as follows:1.The motion equation of axially moving FGM plate is deduced based on the theory of composite thin plate and geometry-displacement equation of small deflection deformation.The influence of in-plane force and axial velocity on the natural frequency and dynamic response of FGM plate is solved and analyzed by harmonic balance method and Galerkin method.The results show that the natural frequency of FGM plate decreases with the increase of material composition index,axial velocity and in-plane pressure,increases with the increase of aspect ratio and in-plane tension,and the variation range of central dynamic deflection of FGM plate increases with the increase of in-plane pressure,aspect ratio,axial velocity,side-thickness ratio and material composition index.In addition,the boundary conditions also have some influence on the natural frequencies and dynamic responses of FGM plates.2.The buckling and flutter characteristics of axially moving FGM plates under different factors are analyzed by Galerkin integral method and generalized eigenvalue method.The results show that the critical buckling and flutter velocities of FGM plates decrease with the increase of material composition index and in-plane pressure;the critical buckling load decreases with the increase of axial velocity;the critical buckling velocities,loads and flutter velocities of FGM plates are the largest under the condition of x-edge fixed y-edge simply supported boundary and the smallest under the condition of four-edge simply supported boundary.3.The analytical solutions of bifurcation buckling,free vibration and dynamic stability boundary of axially moving FGM plates under in-plane periodic loads are solved by Galerkin integral and Bolotin method.The results show that the critical buckling loads and natural frequencies of FGM plates decrease with the increase of material composition index and axial velocity,while the natural frequencies and critical excitation frequencies of FGM plates decrease with the increase of in-plane pressure.The critical excitation frequency and unstable region of FGM plate decrease with the increase of material composition index,axial velocity and aspect ratio,and increase with the increase of aspect ratio.In addition,the buckling critical load,unstable region and critical excitation frequency of FGM plate under x-edge fixed y-edge simply supported boundary condition are the largest,while those under four-edge simply supported boundary condition are the smallest.For the calculation method and process of the above content,this paper uses MATLAB and FORTRAN language to compile the corresponding program package,which can calculate the more accurate results for this paper,and has a certain guiding role in the study of dynamic characteristics such as vibration,buckling,flutter and dynamic stability of axially moving FGM plate structure.