scholarly journals Free vibration of a 2D-FGSW beam based on a shear deformation theory

2020 ◽  
Author(s):  
Vu Thi An Ninh ◽  
Le Thi Ngoc Anh ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Length Direction

A two-dimensional functionally graded sandwich (2D-FGSW) beam model\break formed from three constituent materials is proposed and its free vibration is studied for the first time. The beam consists of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the length and thickness directions by power gradation laws. Based on a third-order shear deformation theory, a beam element using the transverse shear rotation as an independent variable is formulated and employed in the study.  The obtained numerical result reveals that the variation of the material properties in the length direction plays an important role on the natural frequencies and vibration modes  of the beam. The effects of the material distribution and layer thickness ratio on the vibration characteristics are investigated in detail. The influence of the aspect ratio on the frequencies is also examined and discussed.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

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