The Free Vibration Of Functionally Graded Circular Plate With Piezoelectric Surface Layer In Thermal Environment

The piezoelectric material is the link between the general material and the intelligent material.The piezoelectric material under various loads is favored by the scholars in the mechanical research.In addition,Functionally graded materials(FGM)is a new type of functional material that takes into account the advantages of each component of the material,which makes FGM applied widely in the aviation industry,electronics,machinery,nuclear energy and other fields.It is one of the most important contents of engineering mechanics to combine the two materials in the thermal environment and under the control voltage.In this paper,we mainly discuss and analyze the frequency of free vibration in different thermal environment and the change trend of free frequency under the surface pressed layer FGM plate according to the medium thick circular plate model.But the relation between physical parameters of the piezoelectric material and the temperature change is not considered.The some meaningful results are as follows:The main internal capacity includes the following aspects: 1.The governing equations for the free vibration of functionally graded moderately thick circular plates in the thermal environment are derived.A physical model of FGM circular plates under thermal environment is established.Different from the classical plate theory,the influence of the first order transverse shear deformation and the gradient property of the material on the deformation is considered in the analysis.Under the assumption of small amplitude and harmonic vibration,the control equations of the medium thick circular plate on the surface of the surface pressure layer expressed in the ambient temperature are given respectively,and the boundary conditions under various boundaries are given,and the control equation and the boundary conditions are dimensionless.2.Numerical analysis of free vibration to functionally graded moderately thick circular plates is given.The free vibration response of the FGM plate in the surface of the surface piezo layer under different thermal conditions is mainly studied.By using differential quadrature method,the characteristic curves between the first three natural frequencies of the thickness diameter ratio of the FGM thick plate in the thermal environment are obtained.And the data table for controlling frequency changes under thermal environment and different piezoelectric conditions are gained.The influence of functionally graded index,temperature and boundary conditions on vibration characteristics is analyzed and discussed in detail.The natural frequency of the electrothermal environment decreases with the increase of the material component index,the temperature of the environment and the control voltage,and the environmental temperature and the control voltage also have some influence on the dynamic response of the plate.The results of this paper will help people to further understand the vibration characteristics of the structure of functionally graded materials,and help to further improve the research results based on the Mindlin plate theory,and provide effective numerical parameters and analysis results for future researchers.