Sharif Digital Repository

The circulating fluid in natural circulation loops would absorb heat from the hot zone (source) and will transport it to the cold zone (sink) without using of any mechanical pumps or other devices. The fluid density differences in hot and cold zones would lead buoyancy force which is introduced as the body force for the loop. By introducing the one-dimensional conservation equations; mass, momentum and energy in the loop and applying the perturbation method, or linear stability theory, would help us to study the stability of the rectangular natural circulation loop. The conservation equations in transient form were solved using the finite difference method. The results obtained from the... 

In this research, theory of fuzzy sets is used to deal with the uncertain nature of soil parameters and the inaccuracy involved in the analysis simultaneously. Soil parameters are defined using suitable fuzzy sets and the uncertainty inherent in the value of factor of safety is assessed. It is believed that this approach accounts for the uncertainty in soil parameters more realistically compared to the conventional probabilistic approaches reported in the literature. The proposed method is applied to a case study and the results are discussed subsequently  

Linear stability analysis is used to characterize the dynamics of a plane jet by incorporating non-modal stability analysis besides classical global temporal stability analysis. It is explained that similar shapes of different global modes are the result of non-normal characteristics of linearized Navier Stokes equations. Optimal initial disturbances and their eigenfunctions together with transient energy growth are obtained for different time horizons and Reynolds numbers of the jet in the linear unstable configuration. These structures are localized at the upstream of the jet nozzle at the boundary layer. The transient growth of the inlet perturbation in limited time bounds is found in the... 

Based on the transmission line model (TLM), we present an exact and general transfer function formula, useful for both single multiwall carbon nanotube (MWCNT) and MWCNT bundle interconnects. Using the standard parameters for 22-nm technology node we perform the Nyquist stability analysis, to investigate the dependence of the degree of relative stability for both single and bundle interconnects on the number of walls in each MWCNT its geometry and also on the bundle geometry. The numerical results, for 1- to 30-μm long interconnects composed of 3- to 7-wall-CNTs, show that by increasing the length or the outer shell diameter, both single and bundle interconnects become more stable. On the... 

In this study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with... 

A new method is proposed to analyze stability of descriptor systems with multiple commensurate time-delays. In this method, purely imaginary roots of the system are calculated, asymptotic behavior of root path at these roots is studied, and unstable regions of the system in the space of delays are determined. Moreover, the number of roots in each unstable region is calculated. Also necessary and sufficient conditions for τ-stabilizability of these systems are presented. Examples are provided to illustrate the effectiveness and validity of the proposed method. © 2019 The Franklin Institute  

Deep excavation in urban areas can cause instability problems due to significant settlement at the ground surface and large movements at the excavation facing walls. One of the most popular methods used to stabilise these excavations is utilising soil-nailing method. This method has also been widely used to stabilise natural slopes and earth retaining structures. Because of the complexity involved in the mechanism of this stabilising system due to interacting effects of the soil, nails, grout and shotcrete, numerical modelling with high accuracy should be used to analyse the behaviour of the soil-nailed walls. Considering all aspects of soil-structure interaction in the present research, a... 

This paper presents the vibration and stability analyses of an unbalanced rotor mounted on high-static-low-dynamic-stiffness supports. The stiffness of the supports is modeled as symmetric of cubic order. Then a second-order multiple scales method is used for studying the primary resonance of the system. The types of singular points are investigated and phase-plane of the system is plotted using analytical and numerical methods. The difference between analytical and numerical solutions is less than 2 percent. © 2017 Elsevier Masson SAS  

This study addresses the robust stability analysis for an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). Owing to large load changes, microgrid structure reconfiguration, and higher-power demands, the low-frequency (LF) dominant modes of a microgrid stir toward unstable zone and make the system more oscillatory or even unstable. In this study, a robust two-degree-of-freedom (2DOF) decentralised droop controller, which is the combination of the conventional droop with a robust transient droop function, is utilised for each inverter-based DG unit. Unlike conventional tuning of 2DOF droop controllers, a new design procedure is proposed to robustly... 

The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order... 

Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd  

In this paper, we present sufficient conditions to address a larger class of digraphs, including balanced ones, whose members' Laplacian (L) makes L 1L + LTL1 to be positive semi-definite, where L1 is the Laplacian associated with a fully connected equally-edged weighted graphs. This property can be later utilized to introduce an appropriate energy function for stability analysis of flocking algorithms in a larger class of networks with switching directed information flow. Also, some of their properties are investigated in the line of matrix theory and graph theory  

In this paper, important issues that could come up in practice of Active Disturbance Rejection Control (ADRC) due to a common assumption and some inevitable practical restrictions are investigated. The main idea behind ADRC is modeling effects of both internal uncertainties and external disturbances as an extra state called the total disturbance which is timely estimated. In the majority of recent works, it is assumed that time derivative of total disturbance is bounded. First we prove that, beside the system characteristics, the validity of this assumption strongly depends on the tuning parameters, even in the case of simple classes of linear second order systems. Thus, one should be... 

This note considers the effect of different Darcy numbers on the onset of natural convection in a horizontal, fluid-saturated porous layer with uniform internal heating. It is assumed that the two bounding surfaces are maintained at constant but equal temperatures and that the fluid and porous matrix are in local thermal equilibrium. Linear stability theory is applied to the problem, and numerical solutions obtained using compact fourth order finite differences are presented for all Darcy numbers between Da = 0 (Darcian porous medium) and Da → ∞ (the clear fluid limit). The numerical work is supplemented by an asymptotic analysis for small values Da. © 2007 Elsevier Masson SAS. All rights... 

To overcome the problem of magneto hydrodynamic instabilities at the aluminum-cryolite interface in aluminum reduction cells, the use of a simple and efficient model has been suggested. In this paper a new model for evaluation of magneto hydrodynamic instabilities in aluminum reduction cells is proposed. This model is in the form of a wave equation for interfacial oscillations and is constructed based on Shallow Water approximation and linear stability analysis. In this model two terms for linear friction in each molten layer of aluminum and cryolite has been considered and also Lorentz forces in cryolite layer have not been neglected. By accounting of these additional terms in our model,... 

Paralleling power modules is designed to share system loads (stresses) equally to improve system reliability. Due to variations in the parameters in the power converter system, temperature mismatches may occur. These mismatches may lead to unequal life expectancy of individual converters in the total system. It is believed that equalizing the operating temperature of the semiconductor devices may improve total system reliability. In this paper a new thermal-based load-sharing scheme for parallel converters is proposed. In this scheme, the load current is redistributed among parallel converters based on the temperature of the converters. The main goal is to minimize the relative temperature...