Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

2012 ◽  
Vol 18 (3) ◽  
pp. 264-284 ◽  
Author(s):  
B Sobhani Aragh ◽  
E Borzabadi Farahani ◽  
AH Nasrollah Barati
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Natural Frequency ◽  
Frequency Analysis ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Third Order ◽  
Natural Frequency Analysis

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.

The Linear and Nonlinear Bending Analyses of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Based on the Novel Four-Node Quadrilateral Element

2020 ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Numerical Results ◽  
Quadrilateral Element ◽  
Third Order ◽  
Reinforced Composite ◽  
Linear And Nonlinear

This paper presents the linear and nonlinear analyses of functionally graded carbon nanotube- reinforced composite (FG-CNTRC) plates using a four-node quadrilateral element based on the C0-type of Shi’s third-order shear deformation theory (C0-STSDT). Shi’s theory is taking the advantages and desirable properties of the third-order shear deformation theory. Besides, material properties of FG-CNTRC plates are changed from the bottom to top surface and based on the rule of mixture. Numerical results and comparison with other reference solutions suggest that the advantages of present element are accuracy and efficiency in analysis of FG-CNTRC plates. Some nonlinear numerical results of FG-CNTRC plates are also given in this paper and this contributes to providing additional data for future research work.

scholarly journals Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Muneerah Saad AL Nuwairan ◽  
Saira Javed
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Mode Shapes ◽  
Present Formulation ◽  
Third Order ◽  
Node Number

The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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