scholarly journals Free vibration of thick annular sector plate on Pasternak foundation with general boundary conditions

2016 ◽  
Vol 18 (3) ◽  
pp. 1692-1706
Author(s):  
Fanming Liu ◽  
Huimin Liu ◽  
Haoran Bai ◽  
Ranbing Yang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
General Boundary ◽  
Pasternak Foundation ◽  
General Boundary Conditions ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

scholarly journals Free Vibration Of Functionally Graded Carbon Nanotube Reinforced Composite Annular Sector Plate With General Boundary Supports

2018 ◽  
Vol 5 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Fuzhen Pang ◽  
Haichao Li ◽  
Yuan Du ◽  
Yanhe Shan ◽  
Fang Ji
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Ritz Method ◽  
Admissible Function ◽  
Functionally Graded ◽  
General Boundary ◽  
Reinforced Composite ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

Abstract In this paper, an efficient and unified approach for free vibration analysis of the moderately thick functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports is presented by using the Ritz method and the first-order shear deformation theory. For the distribution of the carbon nanotubes in thickness direction, it may be uniform or functionally graded. Properties of the composite media are based on a refined rule of the mixture approach which contains the efficiency parameters. A modified Fourier series is chosen as the basic function of the admissible function to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. To establish the general boundary supports of the annular sector plate, the artificial spring boundary technique is implemented at all edges. The desired solutions are obtained through the Ritz-variational energy method. Some numerical examples are considered to check the accuracy, convergence and reliability of the present method. In addition, the parameter studies of the functionally graded carbon nanotube reinforced composite annular sector plate are carried out as well.

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

Dynamic analysis of annular sector plate with general boundary supports

2013 ◽  
Vol 133 (5) ◽  
pp. 3562-3562
Author(s):  
Dongyan Shi ◽  
Xianjie Shi ◽  
Wen L. Li ◽  
Qingshan Wang
Keyword(s):  
Dynamic Analysis ◽  
General Boundary ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

scholarly journals Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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