Vibration Analysis of Rotating Functionally Gradient Nano Annular Plates in Thermal Environment

LIU Xu; YAO Linquan

doi:10.21656/1000-0887.410090

Volume 41 Issue 11

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LIU Xu, YAO Linquan. Vibration Analysis of Rotating Functionally Gradient Nano Annular Plates in Thermal Environment[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1224-1236. doi: 10.21656/1000-0887.410090

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Vibration Analysis of Rotating Functionally Gradient Nano Annular Plates in Thermal Environment

doi: 10.21656/1000-0887.410090

LIU Xu,
YAO Linquan

School of Rail Transportation, Soochow University,Suzhou, Jiangsu 215131, P.R.China

Funds: The National Natural Science Foundation of China(11572210)

Received Date: 2020-03-30
Rev Recd Date: 2020-10-20
Publish Date: 2020-11-01

Abstract

Abstract

Based on the nonlocal elasticity theory and the Kirchhoff thin plate theory, the vibration frequencies of rotating FGM nano annular plates in thermal environment were studied. Firstly, the differential equations for coupled radial and transverse motions of the rotating FGM nano annular plate under temperature changes and surface forces caused by rotating motions were obtained with the Hamiltonian principle, in turn, the transverse vibration of the plate was solved. Then, with the plane stress method, the axially symmetrical midplane internal forces of the annular plate under the action of centrifugal inertia force and the temperature stress distributed along the radial direction were obtained. After this, the differential equation with variable coefficients was solved with the differential quadrature method. Finally, through numerical simulations, the effects of the innerouter diameter ratio, the functionally gradient parameters, the rotation speed, the nonlocal parameters and the temperature on the dimensionless natural frequencies of the annular plate were analyzed.
- nonlocal theory,
- functionally graded material,
- nano annular plate,
- differential quadrature method,
- natural frequency

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References

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