Torsional vibration of functionally graded carbon nanotube reinforced conical shells

2018 ◽  
Vol 25 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Yaser Kiani
Keyword(s):  
Torsional Vibration ◽  
Conical Shell ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Coupled Equations ◽  
Parametric Studies ◽  
Torsional Frequency ◽  
Generalized Differential

AbstractThe present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

Aeroelastic Analysis of Laminated FG-CNTRC Cylindrical Panels Under Yawed Supersonic Flow

2019 ◽  
Vol 11 (06) ◽  
pp. 1950052 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Farhad Kiani ◽  
Hassan Afshari
Keyword(s):  
Carbon Nanotubes ◽  
Supersonic Flow ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
External Pressure ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Cylindrical Panels ◽  
Generalized Differential

This paper presents a parametric study on aeroelastic stability analysis of multi-layered functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical panels subjected to a yawed supersonic flow. The panel is considered to be composed of different layers reinforced by carbon nanotubes arranged in different directions with various patterns and different volume fractions. Reddy’s third-order shear deformation theory (TSDT) is employed to model the structure and external pressure is estimated based on the linear supersonic piston theory. The set of governing equations and boundary conditions are derived using Hamilton’s principle and are solved numerically using generalized differential quadrature method (GDQM). Convergence and accuracy of the presented solution are confirmed and effect of volume fraction, distributions and orientation of carbon nanotubes (CNTs), yaw angle and geometrical parameters of the panel on the flutter boundaries are investigated. Results of this paper can be considered as a useful tool in design and analysis of supersonic airplanes and missiles.

Buckling Analysis of FGM Thick Beam under Different Boundary Conditions Using GDQM

2012 ◽  
Vol 433-440 ◽  
pp. 4920-4924 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mohammad Ali Bagheri ◽  
Amin Ghobadi
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Graded Materials ◽  
Generalized Differential ◽  
Thick Beam

In this paper, buckling analysis of functionally graded (FG) thick beam under different conditions is presented. Based on the first order shear deformation theory, governing equations are obtained for Thimoshenko beam which is subjected to mechanical loads. In functionally graded materials (FGMs) the material properties obeying a simple power law is assumed to vary through thickness. In order to solve the buckling differential equations, Generalized Differential Quadrature Method (GDQM) is employed and thus a set of eigenvalue equations resulted. For solving this eigenvalue problem, a computer program was developed in a way that the influence of different parameters such as height to length ratio, various volume fraction functions and boundary conditions were included. Non-dimensional critical stress was calculated for simply-simply, clamped-simply and clamped-clamped supported beams. The results of GDQ method were compared with reported results from solving the Finite element too. The comparison showed the accuracy of obtained results clearly in this work.

scholarly journals Dynamics of axially functionally graded conical pipes conveying fluid

2021 ◽  
Vol 37 ◽  
pp. 318-326
Author(s):  
Yuzhen Zhao ◽  
Dike Hu ◽  
Song Wu ◽  
Xinjun Long ◽  
Yongshou Liu
Keyword(s):  
Natural Frequency ◽  
Critical Velocity ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Reduction Factor ◽  
Functionally Graded ◽  
Function Type ◽  
Pipes Conveying Fluid ◽  
Volume Fraction Function ◽  
Conveying Fluid

Abstract In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.

Symmetric Thermo-Electro-Elastic Response of Piezoelectric Hollow Cylinder Under Thermal Shock Using Lord–Shulman Theory

2020 ◽  
Vol 20 (05) ◽  
pp. 2050059
Author(s):  
S. M. H. Jani ◽  
Y. Kiani
Keyword(s):  
Thermal Shock ◽  
Differential Quadrature Method ◽  
Elastic Response ◽  
Governing Equations ◽  
Coupled Equations ◽  
Piezoelectric Hollow Cylinder ◽  
Time Marching ◽  
Generalized Differential ◽  
Lord And Shulman Theory ◽  
Marching Scheme

The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These equations are transformed into the dimensionless ones. With the aid of the generalized differential quadrature method, these equations are discretized in the radial direction. After that, with the aid of the Newmark time marching scheme, the temporal evolutions of the thermo-electro-elastic parameters are obtained. Novel numerical results are presented to obtain the response of the cylinder subjected to a thermal shock using the Lord and Shulman theory of thermoelasticity.

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.

Diagnosis of Type, Location and Size of Cracks by Using Generalized Differential Quadrature and Rayleigh Quotient Methods

2013 ◽  
Vol 43 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Majid Akbarzadeh Khorshidi ◽  
Delara Soltani
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Rayleigh Quotient ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Quadrature Method ◽  
Torsion Spring ◽  
Free Boundary Conditions ◽  
Generalized Differential ◽  
The Relationship

Abstract In this paper, an appropriate and accurate algorithm is pro- posed to diagnosis of lateral or vertical cracks on beam, based on beam natural frequencies. Clamped-free boundary conditions are assumed for the beam. The crack in beam is modelled by without mass torsion spring. Then, the relationship between the beam natural frequencies, location and stiffness of the crack is presented by using the Rayleigh quotient and the governing equation is solved by using generalized differential quadrature method (GDQM). If there is only one crack in the beam, then three natural frequencies are used as inputs to the algorithm and mode shapes corresponding to each the natural frequencies are calculated. Finally, type, location and severity of cracks in beam, are diagnosed.

scholarly journals Thermal Free Vibration Analysis of Temperature-Dependent Functionally Graded Plates Using Second Order Shear Deformation

2011 ◽  
Vol 471-472 ◽  
pp. 133-139 ◽  
Author(s):  
Ali Shahrjerdi ◽  
Faizal Mustapha ◽  
S.M. Sapuan ◽  
M. Bayat ◽  
Dayang Laila Abang Abdul Majid ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Second Order ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Functionally Graded Plates ◽  
Temperature Dependent

This research has been conducted to approach second-order shear deformation theory (SSDT) to analysis vibration characteristics of Functionally Graded Plates (FGP’s). Material properties in FGP's were assumed to be temperature dependent and graded along the thickness using a simple power law distribution in term of the volume fractions of the constituents. FGP was subjected to a linear and nonlinear temperature rise. The energy method was chosen to derive the equilibrium equations. The solution was based on the Fourier series that satisfy the simply supported boundary condition (Navier's method). Numerical results indicated the effect of material composition, plate geometry, and temperature fields on the vibration characteristics and mode shapes. The results revealed that, the temperature field and volume fraction distribution had significant effect on the vibration of FGPs. It was observed the second order theory was very close to the other shear deformation theorem as reported in the literature.

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