Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

Meccanica ◽  
2015 ◽  
Vol 50 (9) ◽  
pp. 2391-2408 ◽  
Author(s):  
Mojtaba Zare ◽  
Reza Nazemnezhad ◽  
Shahrokh Hosseini-Hashemi
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Frequency Analysis ◽  
Analytical Method ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Natural Frequency Analysis

Natural frequency analysis of fluid conveying pipeline with different boundary conditions

2010 ◽  
Vol 240 (3) ◽  
pp. 461-467 ◽  
Author(s):  
Huang Yi-min ◽  
Liu Yong-shou ◽  
Li Bao-hui ◽  
Li Yan-jiang ◽  
Yue Zhu-feng
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Frequency Analysis ◽  
Different Boundary Conditions ◽  
Natural Frequency Analysis

Three-dimensional natural frequency analysis of anisotropic functionally graded annular sector plates resting on elastic foundations

2015 ◽  
Vol 22 (6) ◽  
Author(s):  
Kamran Asemi ◽  
Manouchehr Salehi ◽  
Mehdi Akhlaghi
Keyword(s):  
Natural Frequency ◽  
Frequency Analysis ◽  
Material Properties ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Element Formulation ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Natural Frequency Analysis

AbstractNatural frequency analysis of anisotropic functionally graded material (FGM) annular sector plates on Winkler elastic foundations based on three-dimensional theory of elasticity was investigated. The three-dimensional graded finite element formulation was derived based on the principle of minimum potential energy and the Rayleigh-Ritz method. For an orthotropic FGM, the material properties were assumed to have in-plane polar orthotropy and transverse heterogeneity according to an exponential law, whereas the mass density was assumed to be constant. For an isotropic FGM, material properties varied continuously through the thickness direction according to a power-law distribution, whereas Poisson’s ratio was set to be constant. The effects of material gradient exponents, different sector angles, different thickness ratio, Winkler parameter and two different boundary conditions on the natural frequencies and mode shapes of FGM annular sector plates have been investigated. Numerical solution was compared with the result of an FGM annular circular plate, which showed good agreement.

Natural Frequency Analysis of Multilayer Truncated Conical Shells Containing Quiescent Fluid on Elastic Foundation with Different Boundary Conditions

2021 ◽  
Author(s):  
Reza Paknejad ◽  
Faramarz Ashenai Ghasemi ◽  
Keramat Malekzadeh Fard
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Elastic Foundation ◽  
Conical Shell ◽  
Weight Functions ◽  
Conical Shells ◽  
Different Boundary Conditions ◽  
Fundamental Natural Frequency ◽  
Natural Frequency Analysis ◽  
Quiescent Fluid

In this paper, natural frequency of a multilayer truncated conical composite shell conveying quiescent fluid on elastic foundation with different boundary conditions is investigated and analyzed. The governing equations are presented based on the first-order shear deformation theory. Bernoulli’s equation and velocity potential have been used in the shell-fluid interface to obtain the fluid pressure. The fluid used in this study is considered non-compressible and non-viscous. The beam functions and the Galerkin weight functions method are used to describe and solve the coupled system of differential equations. Three types of boundary conditions are considered to investigate the natural frequency of the conical shells. The results show that the presence of the fluid in the conical shell reduces the fundamental natural frequency values. Also, by changing the semi-vertex conical angle from [Formula: see text] to [Formula: see text] for the simply support boundary conditions, the fundamental natural frequency value for the composite conical shell without and with fluid increases, and the presence of the elastic foundation increases the frequencies of the empty and full-fluid composite conical shells.

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