Three-dimensional static and free vibration analysis of graphene platelet–reinforced porous composite cylindrical shell

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1627-1645 ◽  
Author(s):  
Alireza Rahimi ◽  
Akbar Alibeigloo ◽  
Mehran Safarpour
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Graphene Platelet ◽  
Vibration Behavior ◽  
Reinforced Composite ◽  
Graphene Platelets

Because of promoted thermomechanical performance of functionally graded graphene platelet–reinforced composite ultralight porous structural components, this article investigates bending and free vibration behavior of functionally graded graphene platelet–reinforced composite porous cylindrical shell based on the theory of elasticity. Effective elasticity modulus of the composite is estimated with the aid of modified version of Halpin–Tsai micromechanics. Rule of mixtures is used to obtain mass density and Poisson’s ratio of the graphene platelet–reinforced composite shell. An analytical solution is introduced to obtain the natural frequencies and static behavior of simply supported cylindrical shell by applying the state-space technique along the radial coordinate and Fourier series expansion along the circumferential and axial direction. In addition, differential quadrature method is used to explore the response of the cylindrical shell in the other cases of boundary conditions. Validity of the applied approach is examined by comparing the numerical results with those published in the available literature. A comprehensive parametric study is conducted on the effects of different combinations of graphene platelets distribution patterns and porosity distribution patterns, boundary conditions, graphene platelets weight fraction, porosity coefficient, and geometry of the shell (such as mid-radius to thickness ratio and length to mid-radius ratio) on the bending and free vibration behavior of the functionally graded graphene platelet–reinforced composite porous cylindrical shell. The results of this study provide useful practical tips for engineers designing composite structures.

scholarly journals Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

2021 ◽  
Vol 11 (14) ◽  
pp. 6331
Author(s):  
Mehran Safarpour ◽  
Ali Forooghi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Thermal Conditions ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Total Potential ◽  
Reinforced Composite ◽  
Graphene Platelets ◽  
Generalized Differential ◽  
Minimum Total Potential Energy

In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

scholarly journals Elasticity Solutions for In-Plane Free Vibration of FG-GPLRC Circular Arches with Various End Conditions

2020 ◽  
Vol 10 (14) ◽  
pp. 4695
Author(s):  
Dongying Liu ◽  
Jing Sun ◽  
Linhua Lan
Keyword(s):  
Free Vibration ◽  
Weight Fraction ◽  
Distribution Patterns ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Scaled Model ◽  
Circular Arch ◽  
End Conditions ◽  
Elasticity Solutions ◽  
Graphene Platelets

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

Effect of Porosity on Flexural Vibration of CNT-Reinforced Cylindrical Shells in Thermal Environment Using GDQM

2018 ◽  
Vol 18 (10) ◽  
pp. 1850123 ◽  
Author(s):  
Hamed Safarpour ◽  
Kianoosh Mohammadi ◽  
Majid Ghadiri ◽  
Mohammad M. Barooti
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Flexural Vibration ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Equivalent Material

This article investigates the flexural vibration of temperature-dependent and carbon nanotube-reinforced (CNTR) cylindrical shells made of functionally graded (FG) porous materials under various kinds of thermal loadings. The equivalent material properties of the cylindrical shell of concern are estimated using the rule of mixture. Both the cases of uniform distribution (UD) and FG distribution patterns of reinforcements are considered. Thermo-mechanical properties of the cylindrical shell are supposed to vary through the thickness and are estimated using the modified power-law rule, by which the porosities with even and uneven types are approximated. As the porosities occur inside the FG materials during the manufacturing process, it is necessary to consider their impact on the vibration behavior of shells. The present study is featured by consideration of different types of porosities in various CNT reinforcements under various boundary conditions in a single model. The governing equations and boundary conditions are developed using Hamilton's principle and solved by the generalized differential quadrature method. The accuracy of the present results is verified by comparison with existing ones and those by Navier's method. The results show that the length to radius ratio and temperature, as well as CNT reinforcement, porosity, thermal loading, and boundary conditions, play an important role on the natural frequency of the cylindrical shell of concern in thermal environment.

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