Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (18) : 95-100.

LI Qinglu1, ZHANG Jinghua1, LI Shirong2

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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.

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functionally graded material(FGM) / moderately thick circular plates / free vibration / natural frequency / shooting method

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LI Qinglu1, ZHANG Jinghua1, LI Shirong2. Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method[J]. Journal of Vibration and Shock, 2016, 35(18): 95-100

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