Sharif Digital Repository

The stress distribution on open-ended Carbon Nanotubes (CNTs) embedded in a composite material is considered in this work and an analytical solution for the stress distribution has been obtained. The effects of CNT's thickness and CNT's length on the distribution of stress have been investigated. To find the governing relations, continuity equations of the axisymmetric problem in cylindrical coordinate (r,o,z) are used. Under some assumptions, the governing equations are solved and by using constitutive equations and applying the boundary conditions, an equation which relates the stress applied to the representative volume element with the stress distribution on the CNT, has been found. The... 

In this paper, a relation is introduced that simplifies the determination of the Muskhelishvilis potential function in plane contact problems. The relation is (z)=1/2[p(z)iq(z)], which is correct for all uncoupled-elastic contact problems. This relation is proved in a mathematical way and utilized to obtain the potential function in several contact problems. A complete agreement has been observed between our results and the potential functions that have been obtained from complicated methods in the past. Utilization of the relation simplifies the solution of contact problems and analytical calculation of the stress and displacement fields, which is helpful in the analytical studies of... 

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural... 

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural... 

Supersonic turbulent high-pressure jet flows, which are discharging in low-pressure quiescent ambient, are recognized as imperfectly expanded turbulent jet. Steady-state imperfectly expanded jet flow has been already studied analytically; however, the transient flow has not been thoroughly studied. In the present study, the transient imperfectly expanded jet flow with focus on fuel spray in combustion is investigated analytically employing two-step separation of variables method and Fourier-Bessel expansion. The results are validated using available experimental data. The effects of different parameters such as eddy viscosity and pressure ratio on the behavior of the jet are studied. Results... 

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed... 

One of the main properties of today's distributed and parallel systems, such as mobile ad-hoc networks and grids, is their heterogeneity in the available resources. Further, many applications of such systems are subject to Time/Utility Function (TUF) time constraints for jobs, unavoidable variability in job characteristics and arrivals, and statistical assurance requirements on timeliness behaviors. In this paper, we propose an exact analytical solution for performance evaluation of dynamic policies used for routing of TUF-constrained Firm Real-Time (FRT) jobs among parallel single-processor queues with arbitrary processing rates and capacities. The analytical method can be used for the... 

The upper and lower bound principals of limit analysis are employed to determine the critical loading on solid circular plate with simply supported boundary conditions and subjected to any distributed loading with rotational symmetry. In this study, material behavior follows a rigid perfectly plastic model and yielding obeys the von-Mises criterion. Homotopy analysis method is employed to achieve the analytical solution to the high nonlinear ordinary differential equations governing the problem. This analytic solution has been obtained in terms of convergent series with easily computable terms. The results are verified with the Tresca yield criterion and presented as plots to show the... 

In this study, static pull-in instability of electrostatically-actuated microbridges and microcantilevers is investigated considering different nonlinear effects. Galerkin's decomposition method is utilized to convert the nonlinear differential equations of motion to nonlinear integro-algebraic equations. Afterward, analytic solutions to static deflections of the microbeams are obtained using the homotopy perturbation method. Results are in excellent agreement with those presented in the literature  

In this research, effective length of one-dimensional combustion in a dilute monopropellant spray, constant area and fixed volume chamber is analytically predicted. A new evaporation rate in the form of d k+1 relation is introduced. In the case of controlling vaporization by radiative heat transfer, k is equal to zero, and when molecular processes control the vaporization, k will be equal to one and in some cases vaporization data need the value of k greater than one to fit properly to related equation. Development of this approach can be used in the design of combustion chambers with optimum length and with using vaporization rate of R = R0〈r〉 0 k/〈r〉k. Spray equation and distribution... 

The exponential growth in the semiconductor industry and hence the increase in chip complexity, has led to more power usage and power density in modern processors. On the other hand, most of today's embedded systems are battery-powered, so the power consumption is one of the most critical criteria in these systems. Dynamic Voltage and Frequency Scaling (DVFS) is known as one of the most effective energy-saving methods. In this paper, we propose the optimal DVFS profile to minimize the energy consumption of a battery-based system with uncertain task execution time under deadline constraints using the Calculus of Variations (CoV). The contribution of this work is to analytically calculate the...