Study On The Modal Frequency Of A Functionally Graded Thin-wall Cylindrical Shell

Functionally graded materials,as a new type of functional materials with excellent performance and thermal protection system,are widely favored in the aerospace field.This paper intends to take the functionally gradient cylindrical shell as the research object,simplify the spacecraft thermal protection surface into a cylindrical thin shell.Through theoretical calculations and finite element simulations,a series of studies on the modal frequencies and vibration characteristics of thermally gradient cylindrical thin shells under different boundary conditions during free vibration and thermal environment are carried out.The main research work and results are as follows:First,for the linear mixing law Voigt model,the power-law distribution function was used to layer the functionally graded materials uniformly in the thickness direction,the physical properties of the material at room temperature were analyzed,and the influence of the microstructure such as the volume fraction index of the ceramic on the material properties was discussed.In this paper,the changes of thermophysical properties of functionally graded materials in several typical thermal environments were compared.The results showed that the material properties of the linear temperature field and the nonlinear temperature field were approximately the same,and the changes in the remaining temperature fields were very different.Then,based on the Love thin shell theory,the stress-displacement equation and stress-strain equation of the functionally graded cylindrical shell were established;the energy frequency and Rayleigh-Ritz method were used to derive the modal frequency characteristic equation of the cylindrical shell;on this basis,through numerical methods the modal frequency of the functionally graded cylindrical shell was solved,and then the dynamic model of the functionally graded cylindrical shell was established by using ABAQUS software and verified the feasibility of the model.Meanwhile,the effect of different geometric parameters on the modal frequency of the cylindrical shell was discussed.The results showed that the functionally graded cylindrical shell had little effect on the vibration characteristics when subjected to pressure in the tube.When the length-diameter ratio was changed under different boundary conditions without load,the modal frequency of the functionally graded cylindrical shell changed basically the same,while the modal frequency always increased when the thickness-diameter ratio increased.Finally,considering the effect of temperature on the functionally graded cylindrical shell material,the effects of different thermal environments and different boundary conditions on the modal frequency of the functionally graded cylindrical shell were studied.The results showed that the modal frequency change laws of the linear temperature field and the nonlinear temperature field had a strong consistency.Under the action of the heat flow temperature field,with the increase of the heat flux density and the increase of temperature,the modal frequency did not change significantly.