Sharif Digital Repository

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... 

A fully analytical solution of the classic coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads is presented. Axisymmetric thermal and mechanical boundary conditions are considered in general forms of arbitrary heat transfer and traction, respectively, at the inner and outer radii of the disk. To solve the governing system of equations, an analytical procedure based on the Fourier-Bessel transform is employed. Closed form formulations are presented for temperature and displacement fields. The results of the present formulations are in good agreement with the numerical results available in the literature. The radial distribution and time history... 

In this article, a fully analytical solution of the generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads, based on Lord–Shulman model, is presented. The general forms of axisymmetric thermal and mechanical boundary conditions as arbitrary time-dependent heat transfer and traction, respectively, are considered at the inner and outer radii of the disk. The governing equations are solved analytically using the principle of superposition and the Fourier–Bessel transform. The general closed form solutions are presented for temperature and displacement fields. To validate the solutions, the results of this study are compared with the... 

A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange... 

The elasticity formulation for equations of motion of micro-rotating disks in the presence of angular acceleration as well as the corresponding boundary conditions are developed based on the non-classical continuum theory of couple stress. The system of the boundary value problem is derived on the basis of the variational method. Analytical elasticity solutions to the system of equations are then provided. Based on the elasticity solution, the mechanical responses, including the displacement and stress fields, for varying-speed micro-rotating disks are studied. In a numerical case study, the effect of the couple stresses on the distribution of stress and displacement components are... 

The elasticity formulation for equations of motion of micro-rotating disks in the presence of angular acceleration as well as the corresponding boundary conditions are developed based on the non-classical continuum theory of couple stress. The system of the boundary value problem is derived on the basis of the variational method. Analytical elasticity solutions to the system of equations are then provided. Based on the elasticity solution, the mechanical responses, including the displacement and stress fields, for varying-speed micro-rotating disks are studied. In a numerical case study, the effect of the couple stresses on the distribution of stress and displacement components are... 

In this paper, a refined finite element method (FEM) based on the Carrera unified formulation (CUF) is extended for stress analysis of rotors and rotating disks with variable thickness. The variational form of the 3D equilibrium equations is obtained using the principle of minimum potential energy and solved by this method. Employing the 1D CUF, a rotor is assumed to be a beam along its axis. In this case, the geometry of the rotor can be discretized into a finite number of 1D beam elements along its axis, while the Lagrange polynomial expansions may be employed to approximate the displacement field over the cross section of the beam. Therefore, the FEM matrices and vectors can be written in... 

The small-scale effects on the mechanical responses of micro-rotating disks with angular acceleration are investigated based on the strain gradient theory, as one of the powerful non-classical continuum theories which have been developed to justify the empirical observations of mechanical behavior in small-scale structures and components. The differential equations governing motion of the micro-disk elements in radial and circumferential direction together with the corresponding boundary conditions are derived. Then, an analytical solution is presented for the components of the displacement field which can be used as a base for determination of the components of the stress field. In a... 

In the current paper, vibrational and critical circular speed characteristics of a functionally graded (FG) rotary microdisk is examined considering a continuum nonlocal model called modified couple stress (MCS) model, for the first time in the literature. The generalized differential quadrature (GDQ) approach and variational method are used for deriving and solving the non-classical final relations. The FG size-dependent micro-sized disk’s final relations and corresponding boundary conditions (BCs) are achieved on the basis of the higher-order shear deformation (HSD) model. Then, a parametric analysis has been conducted to analyze the influences of the length scale factor, circumferential,... 

During the varying angular speed timespans of the start or shutdown of rotating machinery, the machinery components may be subjected to intense mechanical loadings which should be taken into account by its fabricator in the designing processes. In the microscale rotating systems, where the angular velocity is typically very high, the importance of this issue is much higher. In this paper, a comprehensive strain-gradient elasticity formulation is presented for functionally graded rotating micro-disks under the effects of varying angular velocity. The gradation of the constituent material along the radial direction can be a helpful option to mitigate the stresses in rotating micro-disks under... 

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential... 

In this research a computer model based on elasto hydrodynamic fluid film lubrication is developed in order to calculate the torque transmission efficiency of a half-toroidal CVT variator. Validation of this model is verified by comparing the experimental and the model results. Sensitivity of torque transmission efficiency to eleven parameters is investigated. These parameters are: dimensionless roller curvature, aspect ratio, half cone angle, fluid viscosity index, pressure constant for Roelands model, input rotational velocity, absolute viscosity at atmospheric pressure, Young modulus of disks and power rollers, Poisson ratio of disks and power rollers, number of power rollers and variator... 

Understanding the time water takes as it moves from rain or snowmelt through the terrestrial system to arrive as stream discharge, or evapotranspiration (ET) is an important hydrologic quantity. We develop a Lagrangian particle tracking method to capture transient residence times from source to either ET or outflow in an integrated hydrologic model. This method is parallel and efficiently captures time evolution of parcels of water in the model and tracks the source of water for hydrograph or ET separation. We demonstrate this model using hypothetical hillslope simulations driven by snow or rain dominated forcing and two different land cover types. We show that land cover and forcing both... 

Negative magnetophoresis is a novel and attractive method for continuous microparticle sorting inside a magnetic medium. In this method, diamagnetic particles are sorted based on their sizes using magnetic buoyancy force and without any labeling process. Although this method provides some attractive features, such as low-cost fabrication and ease of operation, there are some obstacles that adversely affect its performance, especially for biological applications. Most types of magnetic media, such as ferrofluids, are not biocompatible, and the time-consuming process of sample preparation can be threatening to the viability of the cells within the sample. Furthermore, in this method, both the... 

Titanium nitride-carbon nanocomposites are synthesized by the reaction of TiCl4 and NaN3 in supercritical benzene medium that also serves as a carbon source. The as-prepared precursors (SI, SII) are subjected to several heat treatments (SIII-SV). The synthesized nanoparticles are characterized by X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and transmission electron microscopy (TEM). The samples are tested as electrocatalyst for oxygen reduction reaction in an alkaline electrolyte. It is shown that the electrocatalytic properties of the synthesized nanoparticles are...