Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method
LI Qinglu1, ZHANG Jinghua1, LI Shirong2
1.School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China;
2.College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, China
Abstract：The free vibration of FGM moderately thick circular plates was investigated.A FGM plate consisting of metal and ceramic was considered in the study.Based on the geometric equation, physical equation and equilibrium equation of thick plates, taking into account the transverse shearing deformation, the free vibration equation of axisymmetric FGM thick circular plates was derived in terms of the middle surface angles of rotation and lateral displacement.The material properties of the plate were assumed to vary continuously in the thickness direction according to a power law.By using the shooting method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of FGM thick circular plates were obtained numerically.The effects of material gradient property, thickness ratio and boundary conditions on the natural frequencies were discussed in detail.
李清禄1，张靖华1，李世荣2. FGM中厚圆板轴对称自由振动的打靶法求解[J]. 振动与冲击, 2016, 35(18): 95-100.
LI Qinglu1, ZHANG Jinghua1, LI Shirong2. Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(18): 95-100.
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