An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates

2010 ◽  
Vol 92 (10) ◽  
pp. 2591-2605 ◽  
Author(s):  
Chih-Ping Wu ◽  
Hao-Yuan Li
Keyword(s):  
Shear Deformation ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Material

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

2020 ◽  
pp. 107754632095166
Author(s):  
Chih-Chiang Hong
Keyword(s):  
Shear Deformation ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Homogeneous Equation ◽  
Nonlinear Coefficient ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Material

The effects of third-order shear deformation theory and varied shear correction coefficient on the vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation under thermal environment are investigated. The nonlinear coefficient term of displacement field of third-order shear deformation theory is included to derive the fully homogeneous equation under free vibration of functionally graded material cylindrical shells. The determinant of the coefficient matrix in dynamic equilibrium differential equations under free vibration can be represented into the fully fifth-order polynomial equation, thus the natural frequency can be found. Two parametric effects of environment temperature and functionally graded material power law index on the natural frequency of functionally graded material thick cylindrical shells with and without the nonlinear coefficient term of displacement fields are computed and investigated.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

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