On Transverse Vibrations of Functionally Graded Rotating Hollow Disk

2010 ◽  
Author(s):  
Rui Liu ◽  
Hamid Nayeb-Hashemi ◽  
Masoud Olia ◽  
Ashkan Vaziri
Keyword(s):  
Elastic Modulus ◽  
Critical Speed ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Outer Radius ◽  
Functionally Graded ◽  
Distribution Functions ◽  
Rotating Disks ◽  
Disk Radius ◽  
Power Law Function

We studied the stress field and vibration characteristics of functionally graded rotating disks by solving the governing equation of motion using the finite difference scheme. The material was assumed to have a constant Poisson’s ratio with the elastic modulus varying as a power law function of the disk radius. Such a material could be developed by using particle reinforced composites with various reinforcements or reinforcement volume fraction. The results show that the first critical speed of the rotating disk could be increased by using FGMs. The first critical speed is greater for disks having higher elastic modulus at the outer radius. However, the disk may be unstable for certain distribution functions.

Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk With Nonuniform Thickness and Variable Angular Velocity

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Y. Zheng ◽  
H. Bahaloo ◽  
D. Mousanezhad ◽  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Radial Direction ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Outer Radius ◽  
Functionally Graded ◽  
Circumferential Direction ◽  
Stress Fields ◽  
Fiber Reinforced ◽  
Inner Radius ◽  
Nonuniform Thickness

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

Analysis of In-Plane Vibration and Critical Speeds of the Functionally Graded Rotating Disks

2019 ◽  
Vol 11 (02) ◽  
pp. 1950020 ◽  
Author(s):  
Emadoddin Bagheri ◽  
Mostafa Jahangiri
Keyword(s):  
Material Properties ◽  
Critical Speed ◽  
Rotational Velocity ◽  
Free Vibration Analysis ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Graded Index

In this paper, the in-plane free vibration analysis of the functionally graded rotating disks with variable thickness is presented utilizing DQM. It is assumed that the rotational velocity of the disk is constant and the thickness and material properties including modulus of elasticity and density vary along the radial coordinate. The distribution of the forward and backward traveling waves versus the angular velocity is demonstrated for several modal circles and nodal diameters with respect to the fixed and rotating coordinate systems. After presenting the accuracy and convergence of the numerical method, the derived formulation and the solution method are validated by comparing the results with those obtained in the literature for simple rotating disks. Furthermore, the critical speed of the rotating disk is introduced and obtained for different modes. Finally, the effects of the functionally graded index (describes the distribution of material properties) and geometric shape of the disks (thickness profile and radius ratio) on the natural frequencies and critical speed of the disk are presented. It is observed that as the number of nodal diameter increases, the critical speed of the disk consequently decreases and reaches to an asymptotic value. This value is independent of the geometric characteristics of the disk.

scholarly journals Stress and Deformation Analysis of Clamped Functionally graded Rotating Disks with Variable Thickness

2019 ◽  
Vol 23 (1) ◽  
pp. 202-211 ◽  
Author(s):  
Amit K. Thawait ◽  
Lakshman Sondhi ◽  
Shubhashis Sanyal ◽  
Shubhankar Bhowmick
Keyword(s):  
Variable Thickness ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Deformation Analysis ◽  
Rotating Disks ◽  
Distribution Law ◽  
Linear Elastic ◽  
Disk Material ◽  
Stress And Deformation

Abstract The present study reports the linear elastic analysis of variable thickness functionally graded rotating disks. Disk material is graded radially by varying the volume fraction ratios of the constituent components. Three types of distribution laws, namely power law, exponential law and Mori–Tanaka scheme are considered on a concave thickness profile rotating disk, and the resulting deformation and stresses are evaluated for clamped-free boundary condition. The investigation is carried out using element based grading of material properties on the discretized elements. The effect of grading on deformation and stresses is investigated for each type of material distribution law. Further, a comparison is made between different types of distributions. The results obtained show that in a rotating disk, the deformation and stress fields can be controlled by the distribution law and grading parameter n of the volume fraction ratio.

Thermo-mechanical analysis and optimization of functionally graded rotating disks

2020 ◽  
Vol 55 (5-6) ◽  
pp. 159-171
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande ◽  
Luciano Moro
Keyword(s):  
Finite Element ◽  
Equivalent Stress ◽  
Rotating Disk ◽  
Mechanical Analysis ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Rotating Disks ◽  
Maximum Equivalent Stress ◽  
Quadratic Programming Method ◽  
Stress Uniformity

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.

Vibration Response of Functionally Graded Rotating Disk With a Circumferential Crack

2010 ◽  
Author(s):  
Rui Liu ◽  
Hamid Nayeb-Hashemi
Keyword(s):  
Critical Speed ◽  
Crack Depth ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Campbell Diagram ◽  
Circumferential Crack ◽  
Inner Radius ◽  
The Galerkin Method

In this study, the vibration characteristics of a functionally graded rotating hollow disk with the circumferential surface crack are investigated. In order to simplify the problem, the circumferential crack of the rotating hollow disk is modeled as circumferential step indentation. The Galerkin Method is used to obtain the radial and hoop stresses for disks with clamped edge at the inner radius. Finite Difference scheme is adopted to solve the partial differential equation of motion of the rotating hollow disk to obtain the mode shapes and the Campbell Diagram. The first critical speed, which is one of the important parameters limiting the performance of the rotating disk, was obtained from the Campbell Diagram. The results show that the crack will reduce the stiffness and the critical speed of the rotating disk. Critical speed increases with decreasing the distance from inner radius to the crack and decreases with increasing crack depth. Furthermore, considering the functionally graded disk, the distribution of elastic modulus does not change significantly the effects of circumferential cracks on the vibration characteristics of the rotating.

On the mechanical properties of functionally graded materials reinforced by carbon nanotubes

2017 ◽  
Vol 232 (9) ◽  
pp. 1632-1646 ◽  
Author(s):  
Saeed Rouhi ◽  
Seyed H Alavi
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Elastic Modulus ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Single Walled Carbon Nanotubes ◽  
Functionally Graded ◽  
Graded Materials ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In this paper, the elastic properties of functionally graded materials reinforced by single-walled carbon nanotubes are studied. Three different matrices, including steel-silicon, iron-alumina and alumina-zirconia are considered. Besides, the effects of nanotube length, radius and volume fraction on the Young’s modulus of functionally graded matrices reinforced by single-walled carbon nanotubes are investigated. It is observed that short nanotubes not only cannot increase the longitudinal elastic modulus of the matrices, but sometimes decrease their elastic modulus. Of the three selected matrices, steel-silicon matrix would have the most enhancement. Investigation of the effect of nanotube volume fraction on the mechanical properties of nanocomposites shows that increasing the volume fraction of long single-walled carbon nanotube results in increasing the elastic modulus of the nanocomposites.

Modeling Gas–Liquid Flow Between Rotating and Nonrotating Annular Disks

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Irsha Pardeshi ◽  
Tom I-P. Shih
Keyword(s):  
Rotational Speed ◽  
Critical Speed ◽  
Rotating Disk ◽  
Critical Value ◽  
Outer Radius ◽  
Order Model ◽  
Reduced Order ◽  
Gas Liquid Flow ◽  
Gas Penetration ◽  
Annular Disks

When a liquid is forced to flow radially outward in the gap between two coaxial, parallel annular disks—one rotating and one stationary—the liquid occupies the entire gap until the speed of the rotating disk reaches a critical value. Beyond that critical speed, gas from the outer radius starts to enter into the gap, a process referred to as aeration. The higher the rotational speed, the greater is the extent of penetration by the gas into the gap. The extent of gas penetration strongly affects the torque exerted between the two disks because of the large difference in the gas and liquid viscosities. In this study, a reduced-order model is developed to predict the onset of aeration, extent of gas penetration into the gap, and drag torque as a function of the disk's rotational speed, gap between disks, properties of the liquid, and mass flow rate of the liquid forced through the gap. The model developed was validated by comparing predictions with experimental data.

scholarly journals Elasto-Plastic Stresses in a Functionally Graded Rotating Disk

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Babak Haghpanah Jahromi ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Mechanical Response ◽  
Rotating Disk ◽  
Outer Edge ◽  
Outer Radius ◽  
Disk Center ◽  
Functionally Graded ◽  
Von Mises Stress ◽  
Metal Ceramic

A numerical method based on the extension of the variable material property method was developed to obtain the elasto-plastic stress field in a functionally graded (FG) rotating disk. The method was applied to estimate the stress field in a metal–ceramic functionally graded solid disk. To establish the validity of the proposed method, results were compared with finite element results. Unlike uniform rotating disks, where yielding starts from the disk center, plasticity in FG disks can originate at any point. The effect of different metal–ceramic grading patterns as well as the relative elastic moduli and densities of the ceramic and metallic constituents on the developed stresses were studied. Reinforcement of a metal disk with ceramic particles, in both elastic and plastic regimes, can significantly influence the mechanical response of the disk such as the stress distribution and the critical angular velocities corresponding to the onset of plasticity in the disk and plastic disk. Disks with increasing ceramic content from inner to outer radius showed a more uniform von Mises stress distribution for a fixed value of total ceramic content. In contrast, disks with decreasing ceramic content from inner to outer radius had the lowest outer edge displacement for a fixed value of total ceramic content.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

scholarly journals Galerkin Weighted Residual Method for Axially Functionally Graded Shape Memory Alloy Beams

2019 ◽  
Vol 36 (3) ◽  
pp. 331-345
Author(s):  
Z. T. Kang ◽  
Z. Y. Wang ◽  
B. Zhou ◽  
S. F. Xue
Keyword(s):  
Elastic Modulus ◽  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Weighted Residual Method ◽  
Concentrated Load ◽  
Residual Method

ABSTRACTThis paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

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