Natural frequency of FGM circular plate based on physical neutral surface and Levinson′s third order theory

doi:10.19936/j.cnki.2096-8000.20220428.002

Abstract

Abstract: Based on Levinson′s third-order shear theory, the free vibration of functionally graded material (FGM) circular plates was studied by differential quadrature method. Assuming that the properties of FGM were only along the thickness direction of the plate, the governing differential equation of the problem was derived. Then, by using the concept of physical midplane, the tension bending coupling effect in the constitutive equation caused by the transverse non-uniformity of the material was eliminated, simplifying the original complex governing equation. The dimensionless frequency of transverse vibration of FGM circular plate was obtained by DQM, and compared with the natural frequency of FGM circular plate under the first-order shear theory. The effectiveness of DQM method in solving FGM circular plates based on third-order shear theory was illustrated by an example, which enriches the research results of Levinson′s third-order shear theory. The numerical results show that the solution of the first-order shear theory is slightly higher than that of Levinson′s third-order shear theory for clamped FGM circular plates, but the opposite is true for simply supported FGM circular plates. On this basis, the effects of various factors such as material gradient index on the natural frequencies of FGM composite circular plates are discussed in detail.

Key words: functional gradient material, Levinson′s shear theory, physical neutral surface, free vibration, differential quadrature method, composites

CLC Number:

TB332

CHEN Yu, LI Qing-lu, ZHANG Jing-hua. Natural frequency of FGM circular plate based on physical neutral surface and Levinson′s third order theory[J]. COMPOSITES SCIENCE AND ENGINEERING, 2022, 0(4): 11-17.

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