Nonlinear forced vibration of functionally graded carbon nanotube reinforced composite circular cylindrical shells

2020 ◽  
Vol 231 (6) ◽  
pp. 2497-2519
Author(s):  
Zhihua Wu ◽  
Yimin Zhang ◽  
Guo Yao
Keyword(s):  
Carbon Nanotube ◽  
Forced Vibration ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Circular Cylindrical Shells ◽  
Nonlinear Forced Vibration

Nonlinear Torsional Buckling of Functionally Graded Carbon Nanotube Orthogonally Reinforced Composite Cylindrical Shells in Thermal Environment

2020 ◽  
Vol 12 (07) ◽  
pp. 2050072
Author(s):  
Vu Hoai Nam ◽  
Nguyen-Thoi Trung ◽  
Nguyen Thi Phuong ◽  
Vu Minh Duc ◽  
Vu Tho Hung
Keyword(s):  
Carbon Nanotube ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Distribution Law ◽  
Torsional Buckling ◽  
Geometrical Properties ◽  
Reinforced Composite ◽  
Composite Cylindrical Shells

This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.

Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach

2016 ◽  
Vol 24 (6) ◽  
pp. 1123-1144 ◽  
Author(s):  
R Ansari ◽  
J Torabi ◽  
M Faghih Shojaei
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Energy Functional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Annular Plates ◽  
Reinforced Composite

Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature method and periodic differential operators in axial and circumferential directions, respectively, the discretized form of the energy functional is derived. Based on Hamilton’s principle and using the VDQ method, the reduced forms of mass and stiffness matrices are obtained. The comparison and convergence studies of the present numerical method are first performed and then various numerical results are presented. It is found that the volume fractions and functionally grading of carbon nanotubes play important roles in the vibrational characteristics of FG-CNTRC cylindrical, conical shells and annular plates.

scholarly journals Dynamic Analysis of Multi-Stepped Functionally Graded Carbon Nanotube Reinforced Composite Plate with General Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-27
Author(s):  
Kwanghun Kim ◽  
Songhun Kwak ◽  
Yonguk Ri ◽  
Yongsong Paek ◽  
Wonjin Han ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Potential Energy ◽  
Boundary Conditions ◽  
Energy Function ◽  
Forced Vibration ◽  
Potential Energy Function ◽  
Displacement Function ◽  
Functionally Graded ◽  
General Boundary Condition ◽  
Reinforced Composite

This study presents the multi-stepped functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate model for the first time, and its free and forced vibration is analyzed by employing the domain decomposition method. The segmentation technique is employed to discretize the structure along the length direction. The artificial spring technique is applied to the structural boundary and piecewise interface for satisfying the boundary conditions and the combined conditions between subplates. Based on this, the boundary conditions of subdomains could be considered as a free boundary constraint, reducing the difficulty in constructing the allowable displacement function. Since all the structures of subdomains are identical, the allowable displacement functions of them can be uniformly constructed using the two-dimensional ultraspherical polynomial expansion. The potential energy function of the plate is derived from the first-order shear deformation theory (FSDT). The allowable displacement function is substituted into the potential energy function, and then the natural frequencies and mode shapes of the multi-stepped FG-CNTRC plate are decided by using the Rayleigh–Ritz method. The accuracy and reliability of the proposed method are confirmed by the results of the previous literature and finite element method (FEM). On this basis, the influences of the geometric and material parameters on free and forced vibration of the multi-stepped FG-CNTRC plate are also studied.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

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