Sharif Digital Repository

In non-classical micro-beams, the strain energy of the system is determined by the non-classical continuum mechanics. In this study, we consider a closed-loop control methodology for suppressing the vibration of non-classical microscale Euler-Bernoulli beams with nonlinear electrostatic actuation. The non-dimensional form of the governing nonlinear partial differential equation of the system is introduced and converted into a set of ordinary differential equations using the Galerkin projection method. In addition, we prove the observability of the system and we design a state estimation system using the extended Kalman filter algorithm. The effectiveness and performance of the proposed... 

In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton's principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin's method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM)... 

A decentralized servomechanism controller for islanded (autonomous) operation of radial connection of two distributed generation (DG) units is proposed in this paper. Each DG unit utilizes a voltage-sourced converter (VSC) for interface to its dedicated load. The DG units and the loads are to operate in the islanded mode of operation. Each DG unit regulates the voltage of its dedicated load in a decentralized manner. In this paper, it is first shown that the radial connection of two DG units in the islanded mode constitutes an interconnected composite system consisting of two subsystems. Moreover, the paper shows that the overall islanded system can be controlled by the local controllers,... 

The dynamic pull-in voltage as a criterion for the system stability is one of the most important effects considered with the dynamics of microstructures. In this study effect of microbeam electrical resistivity on the pull-in voltage of an electrostatically actuated microbeam is investigated. Assuming Euler-Bernoulli theory for the microbeam, two coupled nonlinear partial differential equations are derived for the beam deflection and voltage. The one parameter Galerkin method is implemented to transform the equations to a set of nonlinear coupled ordinary differential equations. Obtained equations are solved implementing the differential quadrature method (DQM). Variation of dynamic pull-in... 

In this study vibration amplitude, frequency and damping of a microbeam is controlled using a RLC block containing a capacitor, resistor and inductor in series with the microbeam. Applying this method all of the considerable characteristics of the oscillatory system can be determined and controlled with no change in the geometrical and physical characteristics of the microbeam. Euler-Bernoulli assumptions are made for the microbeam and the electrical current through the microbeam is computed by considering the microbeam deflection and its voltage. Considering the RLC block, the voltage difference between the microbeam and the substrate is calculated. Two coupled nonlinear partial... 

An accurate approximate closed-form solution is presented for bending of thin skew plates with clamped edges subjected to uniform loading using the extended Kantorovich method (EKM). Successive application of EKM together with the idea of weighted residual technique (Galerkin method) converts the governing forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of oblique coordinates system. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration step, exact closed-form solutions are obtained for two ODE systems. It is shown that some parameters such as angle of skew plate have an important... 

Stress analysis of thick walled functionally graded (FG) cylindrical pressure vessels subjected to uniform axisymmetric thermo-mechanical loads is presented using Bernstein polynomials. All thermal and mechanical properties except Poisson's ratio of the FG vessels vary through the thickness with arbitrary functions of the radial coordinate. Based on the thermo-elasticity theory, the first law of thermodynamics and axisymmetric assumption, the governing equations of the semi-coupled thermo-elasticity problem reduce to a set of second order boundary value problem. Galerkin method together with Bernstein polynomials is used to obtain solution for the governing equations. The presented method is... 

In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration... 

This paper presents stability analysis of a distributed generation (DG) controller [1], in an islanded mode, based on the Mapping Theorem and the Zero Exclusion Condition, and validates the results based on a laboratory scale experimental setup. The DG unit is interfaced to the host system through a voltage-sourced converter (VSC). The control strategy regulates the load voltage at the desired value in the islanded mode, despite uncertainties in the load parameters. The frequency of the island is controlled in an open loop manner by an internal oscillator. The experimental results show that the controller provides robust voltage control for a wide range of load parameters, and even maintains... 

This paper introduces a new framework included mathematical model and a new software package interfacing two powerful softwares (MATLAB and GAMS) for obtaining the optimal distributed generation (DG) capacity sizing and sitting investments with capability to simulate large distribution system planning. The proposed optimization model allows minimizing total system planning costs for DG investment, DG operation and maintenance, purchase of power by the distribution companies (DISCOs) from transmission companies (TRANSCOs) and system power losses. The proposed model provides not only the DG size and site but also the new market price as well. Three different cases depending on system... 

This Paper presents a model for optimal locating and sizing of Distributed Generation (DG) for congestion management in deregulated electricity market. For reducing the solution space a priority list of candidate buses is formed and then optimal placement and sizing of DG in potential buses is discussed. In order to incorporate stochastic nature of power system in this study, Monte-Carlo method is used to simulate the effect of uncertainty of loads and system on the optimal location and size of the DGs in the network. The proposed method is applied to IEEE Reliability Test System (RTS). The impacts of load uncertainty on optimum DG size and location are studied  

In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field is a superposition of the classical Euler-Bernoulli beam's displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modified... 

This paper presents a long-term dynamic multi-objective model for distributed generation investment. The proposed model optimizes three objectives, namely active losses, costs and environmental emissions and determines the optimal schemes of sizing, sitting of DG units and specially the dynamics of investment over the planning period. The Pareto optimal solutions of the problem are found using a GA algorithm and finally a fuzzy satisfying method is applied to select the optimal solution considering the desires of the planner. The solutions of Pareto optimal front are analyzed to extract general useful information for planners about the appropriate DG technologies and placement schemes. The... 

Distribution systems management is becoming an increasingly complicated issue due to the introduction of new technologies, new energy trading strategies and a new deregulated environment. In the new deregulated energy market and considering the incentives coming from the technical and economic fields, it is reasonable to consider Distributed Generation (DG) as a viable option for systems reinforcement in competition with voltage regulator devices, to solve the lacking electric power supply problem and meet the load growth requirements with a reasonable price as well as the system power quality problems. The problem of optimal placement and size is formulated in two stages; minimization of... 

Aero-thermoelastic analysis of a simply supported functionally graded truncated conical shell subjected to supersonic air flow is performed to predict the flutter boundaries. The temperature-dependent properties of the FG shell are assumed to be graded through the thickness according to a simple rule of mixture and power-law function of volume fractions of material constituents. Through the thickness steady-state heat conduction is considered for thermal analysis. To perform the stability analysis, the general nonlinear equations of motion are first derived using the classical Love's shell theory and the von Karman-Donnell-type of kinematic nonlinearity together with the linearized... 

A linear time-invariant (LTI) robust servomechanism controller for islanded (autonomous) operation of a distributed generation (DG) unit and its local load is proposed. The DG unit utilizes a voltage-sourced converter (VSC) as the interface medium. The controller design is obtained by introducing a new optimal controller design procedure, in conjunction with a proposed non-conservative robustness constraint. The proposed controller utilizes 1) an internal oscillator for frequency control and 2) a robust servomechanism controller (RSC) to regulate the island voltage. Despite uncertainty of the load parameters, the proposed controller guarantees robust stability and pre-specified performance... 

In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value is calculated based on the 2G, 3D neutron diffusion theory. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of the neutron diffusion equation is performed based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured tetrahedron elements. Using power iteration method, neutron flux and corresponding eigen-value are obtained. The results are then benchmarked against the valid results for VVER-1000 (3D) benchmark problem. In the second stage, the neutron noise equation is solved using GFEM and... 

Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi-analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element-free Galerkin (EFG) mesh-less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity... 

In the present study, the comparison between the results obtained from the linear and quadratic approximations of the Galerkin Finite Element Method (GFEM) for neutronic reactor core calculation was reported. The sensitivity analysis of the calculated neutron multiplication factor, neutron flux and power distributions in the reactor core vs. the number of the unstructured tetrahedron elements and order of the considered shape function was performed. The cost of the performed calculation using linear and quadratic approximation was compared through the calculation of the FOM. The neutronic core calculation was performed for both rectangular and hexagonal geometries. Both the criticality and... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the...