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.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

2019 ◽  
Vol 233 (10) ◽  
pp. 2140-2159 ◽  
Author(s):  
Ehsan Arshid ◽  
Ali Kiani ◽  
Saeed Amir
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Sensors And Actuators

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

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 Response of Functionally Graded Material Plate under Thermomechanical Load Subjected to Various Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Manish Bhandari ◽  
Kamlesh Purohit
Keyword(s):  
High Temperature ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Light Metal ◽  
Functionally Graded ◽  
Numerical Results ◽  
Element Formulation ◽  
Power Law Distribution

Functionally graded materials (FGMs) are one of the advanced materials capable of withstanding the high temperature environments. The FGMs consist of the continuously varying composition of two different materials. One is an engineering ceramic to resist the thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. In the present study, the properties of the FGM plate are assumed to vary along the thickness direction according to the power law distribution, sigmoid distribution, and exponential distribution. The fundamental equations are obtained using the first order shear deformation theory and the finite element formulation is done using minimum potential energy approach. The numerical results are obtained for different distributions of FGM, volume fractions, and boundary conditions. The FGM plate is subjected to thermal environment and transverse UDL under thermal environment and the response is analysed. Numerical results are provided in nondimensional form.

TORSIONAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS WITH TEMPERATURE-DEPENDENT PROPERTIES

2013 ◽  
Vol 14 (01) ◽  
pp. 1350048 ◽  
Author(s):  
JIABIN SUN ◽  
XINSHENG XU ◽  
C. W. LIM
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Effective Properties ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Accurate Solution ◽  
Functionally Graded ◽  
Torsional Buckling ◽  
Temperature Dependent Properties ◽  
Transverse Boundary

Based on Hamilton's principle, a new accurate solution methodology is developed to study the torsional bifurcation buckling of functionally graded cylindrical shells in a thermal environment. The effective properties of functionally graded materials (FGMs) are assumed to be functions of the ambient temperature as well as the thickness coordinate of the shell. By applying Donnell's shell theory, the lower-order Hamiltonian canonical equations are established, from which the eigenvalues and eigenvectors are solved as the critical loads and buckling modes of the shell of concern, respectively. The effects of various aspects, including the combined in-plane and transverse boundary conditions, dimensionless geometric parameters, FGM parameters and changing thermal surroundings, are discussed in detail. The results reveal that the in-plane axial edge supports do have a certain influence on the buckling loads. On the other hand, the transverse boundary conditions only affect extremely short shells. With increasing thermal loads, the material volume fraction has a different influence on the critical stresses. It is concluded that the optimized FGM mixtures to withstand thermal torsional buckling are Si 3 N 4/SUS304 and Al 2 O 3/SUS304 among the materials studied in this paper.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

Interaction Between Thermal Field and Two-Dimensional Functionally Graded Materials: A Structural Mechanical Example

2019 ◽  
Vol 11 (10) ◽  
pp. 1950099 ◽  
Author(s):  
Ye Tang ◽  
Shun Zhong ◽  
Tianzhi Yang ◽  
Qian Ding
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Graded Materials ◽  
Promising Strategy ◽  
Generalized Differential ◽  
Euler Bernoulli Beam

The buckling and free vibration of a Euler–Bernoulli beam composed of two-directional functionally graded materials (FGMs) in thermal environment are analyzed. The material properties and temperature distributions are considered to be continuously varied along both axial and thickness directions. Such two-directional FGMs provide the basis of a promising strategy to tune the dynamic behavior of a structure in a controlled fashion, achieving tunable response as desired. The dynamic equation of the beam and relevant boundary conditions are derived based on Hamilton’s principle. The generalized differential quadrature method is used for determining the exact buckling configuration and the natural frequencies of the beam with different boundary conditions. Numerical results are presented to examine the effects of material gradations on the critical buckling temperature. It is concluded that both temperature change and material properties have significant influences on the natural frequency, which suggests that it is possible to tailor or tune the dynamic behaviors of a beam by using man-made FGMs in a complex environment.

Three-dimensional transient analysis of functionally graded cylindrical shells subjected to asymmetric dynamic pressure

2013 ◽  
Vol 20 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Masoud Tahani ◽  
Ali Reza Setoodeh ◽  
Ehsan Selahi
Keyword(s):  
Boundary Conditions ◽  
Present Method ◽  
Transient Analysis ◽  
Dynamic Pressure ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Functionally Graded

AbstractThis paper presents an efficient and accurate numerical method based on the three-dimensional (3-D) elasticity theory for the transient analysis of functionally graded (FG) hollow cylindrical shells subjected to asymmetric dynamic pressure. The Fourier expansion is employed to describe the displacement components and dynamic pressure in the tangential direction. In addition, the layerwise theory is used to accurately account for the displacement components in the radial direction. The equations of motion and the related boundary conditions are derived using Hamilton’s principle. Then, differential quadrature method (DQM) is implemented to discretize the resulting equations in the both spatial and time domains. The convergence, accuracy and performance of the present method are established through the convergence study and comparison with available results in the literature. Also, the effects of different parameters such as thickness-to-inner radius ratio and boundary conditions on the dynamic behavior of hollow FG cylinders are investigated. The present method can accurately predict transient displacement and stress with less computational efforts.

High-Accuracy Approach for Thermomechanical Vibration Analysis of FG-Gplrc Fluid-Conveying Viscoelastic Thick Cylindrical Shell

2020 ◽  
Vol 12 (07) ◽  
pp. 2050073
Author(s):  
Alireza Rahimi ◽  
Akbar Alibeigloo
Keyword(s):  
Cylindrical Shell ◽  
Temperature Gradient ◽  
Boundary Conditions ◽  
Axial Load ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Negative Influence ◽  
Functionally Graded ◽  
The Impact

High importance of fluid-conveying structures in multifarious engineering applications arises the necessity of enhancing the mechanical characteristics of these systems in an effective way. Accordingly, this paper is concerned with vibration performance of functionally graded graphene-platelets reinforced composite (FG-GPLRC) fluid-conveying viscoelastic cylindrical shell surrounded by two-parameter elastic substrate and exposed to temperature gradient and axial load within the context of refined higher order shear deformation theory (RHSDT) including trapezoidal shape factor. Generalized differential quadrature method (GDQM) is employed to solve differential equations of motion for different cases of boundary conditions. The fourth-order Runge–Kutta technique is utilized to determine the time response of the system. Validity of the results is verified through comparison with those presented in the published articles. Comprehensive parametric analysis is performed to reveal the impact of fluid-flow velocity, distribution patterns of GPL, different forms of applied temperature gradient, different boundary conditions, viscoelasticity coefficient, geometrical dimensions of the shell as well as graphene-sheets on the vibration of the system. The numerical results demonstrate that negative influence of applying compressive axial load and rising temperature gradient on the vibrational response of the system can be alleviated when the system is exposed to sinusoidal form of temperature rise with proper power-index.

scholarly journals Analysis of Cylindrical Shells Using Generalized Differential Quadrature

1997 ◽  
Vol 4 (3) ◽  
pp. 193-198 ◽  
Author(s):  
C.T. Loy ◽  
K.Y. Lam ◽  
C. Shu
Keyword(s):  
Fluid Dynamics ◽  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Generalized Differential

The analysis of cylindrical shells using an improved version of the differential quadrature method is presented. The generalized differential quadrature (GDQ) method has computational advantages over the existing differential quadrature method. The GDQ method has been applied in solutions to fluid dynamics and plate problems and has shown superb accuracy, efficiency, convenience, and great potential in solving differential equations. The present article attempts to apply the method to the solutions of cylindrical shell problems. To illustrate the implementation of the GDQ method, the frequencies and fundamental frequencies for simply supported-simply supported, clamped-clamped, and clamped-simply supported boundary conditions are determined. Results obtained are validated by comparing them with those in the literature.

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