Free Vibration Of Functionally Graded Moderately Thick Circular Plates In Thermal Environment

Functionally graded materials(FGM)are a kind of new functional materials,taking advantage of the merits of constituent materials adequately which has been found wider application foreground in many fields such as aerospace,electricity,machinery,nuclear energy and so on.It is great important to analyze the changes of the free vibration frequency of FGM and the problems of the change of the free vibration frequency of FGM which have been extensively investigated and become one of the important issues in engineering mechanics.In this thesis,for the model of FGM moderately thick circular plates,a more comprehensive study,especially quantitative research of the frequency response in different environments is carried out,and then some meaningful results are obtained.The main contents of it are as follows:1.The governing equations for free vibration of functionally graded moderately thick circular platesThe material properties of the plate are assumed to vary continuously in the thickness direction according to a power law.The physical model of FGM plates is established in thermal environment.Based on the first order shear plate theory,the basic governing equations for the free vibration of moderately thick circular plates in thermal environment are given.It is different from the classical plate theory,because the influence of the first order transverse shear deformation and the gradient properties of the material on the deformation are considered in the analysis.Under the assumption of small deformation and harmonious vibration,the governing equations of moderately thick circular plates expressed by the mode shape function in room temperature and thermal environment are obtained respectively.At the same time,the boundary conditions under different boundary conditions are given.And then the governing equations and boundary conditions are normalized.2.Numerical analysis of free vibration of functionally graded platesIn this thesis,the vibration response of FGM medium-thickness circular plate in different environment is analyzed emphatically.In order to obtain accurate numerical results,this thesis uses the shooting method of numerical solution to obtain the characteristic curves of the first three natural frequencies and the thickness-to-diameter ratio of FGM plates.The effects of the function gradient index,temperature and boundary conditions on the vibration characteristics are analyzed and discussed in detail.The numerical results indicate natural frequency decreases monotonically with the increase of the thickness diameter ratio and the gradient index of the plate,whether it is a simply supported plate,a clamped plate or a free plate under room temperature.In the thermal environment,both the uniform temperature rise and the non-uniform temperature rise,under the three boundary conditions,the frequency of the first three orders will decrease with the increase of temperature,and the first-order frequency has a strong nonlinearity.When the properties are correlated with the temperature,the change trend of the free vibration frequency will change with the change of the function gradient index.The research results will be helpful to further understand the vibration characteristic of FGM structure and improve the research results based on Mindlin plate theory.This thesis provides effective numerical parameters and analysis results for future researchers.