The Vibration Characteristics Of Elastic Thin FGM Circular Plate Based On The Functions Of Different Gradient Modes

Since the 1950s, along with the rapid development of science and technology, it has been unable to meet the original materials and nature, and to seek out and develop new varieties of different, unique properties of the material, in particular in the ultimate environment (Ultra-high temperature, ultra-low-temperature, EHV, Seattle and high vacuum, and so on) the work of the parts require a special performance. Countries in the world in the long-term research on the basis of traditional materials, in addition to more in-depth engineering technologies improve the existing materials, from the succession theory put forward many new material concepts, and in the efforts of some in practice with special properties of new materials, and to meet the special circumstances of various parts of the performance requirements. Has been developed for people along the structure and properties of space are continuous changes in the FGM, because of this new material's fine characteristics, it is emerging more and broad prospects. Therefore this study meaningful1. Description of the problem and the basic equationsConsidered a circular FGM plate, the r-θplanar surface of the plate in the coincidence, the axis of z perpendiculars to the plate in the face, and has the same direction as the material gradient changes. 2 Derivation and Solution of the equation in different gradient mode 2.1 Expressions of elastic modulus E ( z ) and densityρ( z)2.1.1 Elastic modulus and density in the power function model2.1.2 Elastic modulus and density in the e exponential function model2.2 Geometric deformation equation 2.3 Physics equation2.4 Moments expression2.4.1 Moments expression in the power function model 2.4.2 Moments expression in e exponential function mode 2.5 Kinetic equations 3 Natural frequency of the clamped circular plate By the boundary conditions Table 3 be solved, then get the natural frequency of circular plate in different gradient mode. 4 Natural frequencies of the SR circular plate By the boundary conditions Because C n, E n not identically equal to zero Table 4 be solved, then the natural frequency expression can be get corresponding the same to the clamped boundary conditionsFinally, by the examples of the plate, we discuss the inherent frequency bands with a gradient index changes and different gradient mode, different material combinations'effects to the natural frequency of the first order. The results show that the changes in its gradient will have a greater impact on he natural frequency of the first order, under the matching of different materials, a natural frequency bands can exist between the large gap, and different materials'matching can affect FGM plate's inherent attributes, and the e index gradient mode performs more obvious.