The present study deals with the elastic analysis of CONCAVE THICKNESS ROTATING DISKs made of functionally graded materials (FGMs).The analysis is carried out using element based gradation of material properties in radial direction over the discretized domain. The resulting deformation and stresses are evaluated for free-free boundary condition and the effect of grading index on the deformation and stresses is investigated and presented. The results obtained show that there is a significant reduction of stresses in FGM DISKs as compared to homogeneous DISKs and the DISKs modeled by power law FGM have better strength.

The analysis of the bending behavior of ROTATING porous DISKs with exponential THICKNESS variation consisting of viscoelastic functionally graded material is illustrated. The study of bending in the porous DISK was done using the first-order shear deformation theory. The porous DISK is under the effect of a combination of mechanical stresses and thermal distribution. All material factors for the porous DISK change across the THICKNESS as a power law of radius. To solve the mathematical structure by using the semi-analytical technique for displacements in the porous DISK, and then to treat the structure model with viscoelastic material by the correspondence principle and Illyushin’s approximation manner. Numerical outcomes including the effect of porosity parameter, inhomogeneity factor, and relaxation time are presented with three different sets of boundary conditions for the solid and hollow DISKs. A comparison between porous and perfect DISK with numerous values of porosity parameters and different inhomogeneity factors have been shown to emphasize the importance of complex mathematical structure in modern engineering mechanical designs.

This paper is dealing with the Elastoplastic analysis of ROTATING DISKs of variable THICKNESS made of functionally graded materials based on Tresca's yield criterion. To do so, the governing equations of ROTATING annular DISKs are established based on the elasticity theory. Then, using Tresca's yield criterion and the elastic-perfectly plastic flow law, the displacement equations and stresses are obtained in the plastic region. In order to find the effects of the shape of the DISK PROFILE on its stress distribution, the THICKNESS of the DISK cross-section is supposed to vary as an exponential function of the radius. In addition, considering different places at which the yielding starts, the process of expanding the plastic flow is investigated. The obtained results are validated against those reported for homogeneous as well as constant THICKNESS FGM DISKs, showing good agreement. The findings also demonstrate that taking the variable THICKNESS for the DISK cross-section into account has a significant effect on the stress distribution and prediction of the place where the yielding initiate.

The present study is an attempt to analyze the yield threshold in a ROTATING variable-THICKNESS DISK made of functionally graded material (FGM) based on the Tresca yield criterion. The analysis was performed based on the small deformation theory and for the plane stress state. The modulus of elasticity, density and yield stress were assumed to be a power function of the radial coordinate. The Poisson’ s ratio due to slight variations in engineering materials is assumed constant, and the equilibrium equation governing the ROTATING DISK was solved analytically. In addition to the type of material, the DISK cross section PROFILE can affect the distribution of stress fields. The THICKNESS of the DISK cross-section varies in the radial direction by a power function. In the present analysis, various states are considered for onset yield and commencement of plastic flow. For evaluation and validation, the results of the study are compared to similar results related to specific states (homogeneous and functionally graded constant-THICKNESS DISK) investigated in previous references. The results show that considering variable THICKNESS for DISK section has a significant effect on the stress level and the prediction of onset yield point.

In this article, thermo-elastic and creep evolution behaviour of ferritic steel ROTATING DISKs with variable THICKNESS are investigated. Four THICKNESS PROFILEs of uniform, convex, CONCAVE and linear are considered for the DISK geometry. The material creep constitutive model is defined by the Θ projection concept, based on the experimental results existing in the literature. Loading applied is due to the inertial body force caused by the rotation and a constant temperature field throughout the DISK. To achieve history of stresses and displacements, a numerical procedure using finite difference and Prandtl-Reuss relations is used. Stress and deformation histories are calculated using successive elastic solution method. In order to verify the solution approach, both composite and aluminum ROTATING DISKs were taken into account and the thermo-elastic and time-dependent creep behaviours for composite as well as the former for aluminum were obtained. Results from the current study were found to be in very good agreement with those available from literature in the area. It was shown that convex THICKNESS PROFILE DISKs display the least creep displacement, creep effective and circumferential stresses. Additionally, constant and CONCAVE THICKNESS PROFILEs were positively correlated with time while for linear and convex ones, it was found to have an inverse trend.

In this paper energy method is used to calculate rotor response with loose ROTATING DISK on it. System equation of motion is obtained based on energy method and Lagrange equation. Mathematical modeling of loose DISK in a rotor bearing system has resulted in terms similar to unbalance and gyroscopic effect in the system equation of motion. The effect of loose DISK axial position and orthotropic bearing has been considered in this investigation. By assuming that shaft and loose DISK are always in contact, the results of these study shows that clearance between loose DISK and shaft, shaft speed, mass and mass moment of inertia of DISK have a major effect on a rotor response and beating phenomena.

In this article, it is aimed to address one of Ostwald-de Waele fluid problems that either, has not been addressed or very little focused on. Considering the impacts of heat involving in the Non-Newtonian flow, a variant THICKNESS of the DISK is additionally considered which is governed by the relation z = a (r/RO+1)-m. The ROTATING Non-Newtonian flow dynamics are represented by the system of highly nonlinear coupled partial differential equations. To seek a formidable solution of this nonlinear phenomenon, the application of the method of lines using von Ká rmá n’ s transformation is implemented to reduce the given PDEs into a system of nonlinear coupled ordinary differential equations. A numerical solution is considered as the ultimate option, for such nonlinear flow problems, both closed-form solution and an analytical solution are hard to come by. The method of lines scheme is preferred to obtain the desired solution which is found to be more reliable and in accordance with the required physical expectation. Eventually, some new marvels are found. Results indicate that, unlike the flat ROTATING DISK, the local radial skin friction coefficients and tangential decrease with the fluid physical power-law exponent increases, the peak in the radial velocity rises which is significantly distinct from the results of a power-law fluid over a flat ROTATING DISK. The local radial skin friction coefficient increases as the DISK THICKNESS index
increases, while local tangential skin friction coefficient decreases, the local Nusselt number decrease, both the THICKNESS of the velocity and temperature boundary layer increase.

Vibration analysis of ROTATING DISKs is one of the most important problems in turbomachines. In this study, a new method has been presented which analyzed the radial vibration of a turbo-pump ROTATING DISK carrying two annular concentrated masses located on the DISK and at its end. Natural frequencies have been calculated in different ROTATING speeds, then results have been compared with each other. The effects of concentrated masses position and intensity on natural frequencies have been investigated. The results show that concentrated masses always have been decreased the value of first natural frequency, but in the case of second and third natural frequencies, depending on the mass concentration magnitude and its position, the magnitude of natural frequency has been increased or decreased. The vibration of the ROTATING DISK without considering the concentrated mass, was examined. Then the resulting solution was generalized for two connected DISKs in internal concentrated mass location. The effect of concentrated masses, one on the DISK body and the other on the outside of the DISK, is considered as boundary conditions in the two DISK Equations. The results show that increasing in angular velocity of ROTATING DISK reduces the natural frequency. Concentrated masses always reduce the first natural frequency. At the second and third natural frequencies, concentrated masses may increase or decrease the natural frequency, which depends on the value and position of concentrated mass. Concentrated mass has the most impact when it is in a position that has the most radial displacement.

This article presents an exact solution for an axisymmetric functionally graded piezoelectric (FGP) ROTATING DISK with constant THICKNESS subjected to an electric field and thermal gradient. All mechanical, thermal and piezoelectric properties except for Poisson's ratio are taken in the form of power functions in radial direction. After solving the heat transfer equation, first a symmetric distribution of temperature is produced. The gradient of displacement in axial direction is then obtained by assuming stress equation in axial direction to be zero. The electric potential gradient is attained by charge and electric displacement equations. Substituting these terms in the equations for the dimensionless stresses in the radial and circumferential directions yield these stresses and using them in the mechanical equilibrium equation a nonhomogeneous second order differential equation is produced that by solving it, the dimensionless displacement in radial direction can be achieved. The study results for a FGP ROTATING hollow DISK are presented graphically in the form of distributions for displacement, stresses and electrical potential.