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eigenvalues-and-eigenfunctions
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Continuum modelling of a circular planar array of coupled microwave oscillators
, Article European Microwave Week 2009, EuMW 2009: Science, Progress and Quality at Radiofrequencies, Conference Proceedings - 39th European Microwave Conference, EuMC 2009, 28 September 2009 through 2 October 2009, Rome ; 2009 , Pages 1349-1352 ; 9782874870118 (ISBN) ; Banai, A ; Sharif University of Technology
Abstract
in this paper the phase distribution in an array of coupled oscillators arranged on a circular surface is discussed. Coupling is considered to be weak and each oscillator is coupled to its four nearest neighbours. In a continuum limit where the number of oscillators goes to infinity a theoretical formulation in polar coordinates is proposed to describe the dynamic behaviour of phases of the array elements. A Green's function for phase distribution of the array is proposed in terms of its normalized eigenfunctions. Beam steering can be done via detuning the edge oscillators. © 2009 EuMA
Dynamic behavior and transient stability analysis of fixed speed wind turbines
, Article Renewable Energy ; Volume 34, Issue 12 , 2009 , Pages 2613-2624 ; 09601481 (ISSN) ; Parniani, M ; Sharif University of Technology
Abstract
This paper analytically investigates the dynamic behavior of fixed speed wind turbines (FSWTs) under wind speed fluctuations and system disturbances, and identifies the nature of transient instability and system variables involved in the instability. The nature of transient instability in FSWT is not similar to synchronous generators in which the cause of instability is rotor angle instability. In this paper, the study of dynamic behavior includes modal and sensitivity analysis, dynamic behavior analysis under wind speed fluctuation, eigenvalue tracking, and using it to characterize the instability mode, and investigating possible outcomes of instability. The results of theoretical studies...
Robust stability analysis of distributed-order linear time-invariant systems with uncertain order weight functions and uncertain dynamic matrices
, Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 139, Issue 12 , 2017 ; 00220434 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
Abstract
Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex...
Optimal design of two-dimensional porosity distribution in shear deformable functionally graded porous beams for stability analysis
, Article Thin-Walled Structures ; Volume 120 , 2017 , Pages 81-90 ; 02638231 (ISSN) ; Arghavani, J ; Sharif University of Technology
Abstract
In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained....
Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors
, Article Physica E: Low-Dimensional Systems and Nanostructures ; Volume 94 , 2017 , Pages 31-46 ; 13869477 (ISSN) ; Ceballes, S ; Abdelkefi, A ; Sharif University of Technology
Abstract
A nonlocal continuum-based model is derived to simulate the dynamic behavior of bridged carbon nanotube-based nano-scale mass detectors. The carbon nanotube (CNT) is modeled as an elastic Euler-Bernoulli beam considering von-Kármán type geometric nonlinearity. In order to achieve better accuracy in characterization of the CNTs, the geometrical properties of an attached nano-scale particle are introduced into the model by its moment of inertia with respect to the central axis of the beam. The inter-atomic long-range interactions within the structure of the CNT are incorporated into the model using Eringen's nonlocal elastic field theory. In this model, the mass can be deposited along an...
Fully distributed cooperative secondary frequency and voltage control of islanded microgrids
, Article IEEE Transactions on Energy Conversion ; Volume 32, Issue 2 , 2017 , Pages 675-685 ; 08858969 (ISSN) ; Sadati, N ; Hamzeh, M ; Sharif University of Technology
Abstract
This paper proposes a new distributed cooperative secondary control for both frequency and voltage restoration of an islanded microgrid with droop-controlled, inverter-based distributed generations (DGs). Existing distributed methods commonly design secondary control based on the minimum real part of the nonzero Laplacian matrix eigenvalues related to the microgrid communication graph, which, however, is global information. In contrast to the existing distributed methods, in this paper we design a fully distributed adaptive control based on the dynamic model of DG units and on information from neighboring units. Therefore, the proposed control scheme increases the system reliability,...
A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms
, Article Nonlinear Analysis, Theory, Methods and Applications ; Volume 156 , 2017 , Pages 1-16 ; 0362546X (ISSN) ; Torabi Tehrani, H ; Sharif University of Technology
Abstract
We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−c, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d0. In addition, in case c
Dynamic response of thin plates on time-varying elastic point supports
, Article Structural Engineering and Mechanics ; Volume 62, Issue 4 , 2017 , Pages 431-441 ; 12254568 (ISSN) ; Estekanchia, H. E ; Sharif University of Technology
Techno Press
2017
Abstract
In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where...
A shell model for free vibration analysis of carbon nanoscroll
, Article Materials ; Volume 10, Issue 4 , 2017 ; 19961944 (ISSN) ; Ahmadian, M. T ; Asghari, M ; Pugno, N. M ; Sharif University of Technology
Abstract
Carbon nanoscroll (CNS) is a graphene sheet rolled into a spiral structure with great potential for different applications in nanotechnology. In this paper, an equivalent open shell model is presented to study the vibration behavior of a CNS with arbitrary boundary conditions. The equivalent parameters used for modeling the carbon nanotubes are implemented to simulate the CNS. The interactions between the layers of CNS due to van der Waals forces are included in the model. The uniformly distributed translational and torsional springs along the boundaries are considered to achieve a unified solution for different boundary conditions. To study the vibration characteristics of CNS, total energy...
Ictal EEG signal denoising by combination of a semi-blind source separation method and multiscale PCA
, Article 2016 23rd Iranian Conference on Biomedical Engineering and 2016 1st International Iranian Conference on Biomedical Engineering, ICBME 2016, 23 November 2016 through 25 November 2016 ; 2017 , Pages 226-231 ; 9781509034529 (ISBN) ; Hajipour Sardoubie, S ; Shamsollahi, M. B ; Sharif University of Technology
Abstract
Contamination of ictal Electroencephalogram (EEG) signals by muscle artifacts is one of the critical issues related to clinically diagnosing seizure. Over the past decade, several methods have been proposed in time, frequency and time-frequency domain to accurately isolate ictal EEG activities from artifacts. Among denoising approaches Canonical Correlation Analysis (CCA) and Independent Component Analysis (ICA) are widely used. Denoising based on Generalized EigenValue Decomposition (GEVD) is one of the Semi-Blind Source Separation (SBSS) methods which has been recently proposed. In the GEVD-based method, a couple of time-frequency covariance matrices are used. These time-frequency (TF)...
Deriving surface impedance for 2-d arrays of graphene patches using a variational method
, Article IEEE Journal of Quantum Electronics ; Volume 53, Issue 1 , 2017 ; 00189197 (ISSN) ; Tavakol, M. R ; Khavasi, A ; Sharif University of Technology
Abstract
In this paper, we extract the fundamental resonant mode of a graphene patch using a variational method. We use 2-D eigenvalue problem obtained from the integral equation governing the surface current on graphene patterns under quasi-static approximation. To compute the eigenvalues, we propose three trial eigenfunctions, which meet the boundary conditions. We investigate the accuracy of these eigenfunctions with comparing to the results obtained by full wave simulations. Finally, we analyze square-lattice arrangements of graphene patches using the most accurate proposed eigenfunction and derive a very accurate surface impedance for it. The proposed surface impedance is much more precise than...
The algebraic connectivity of a graph and its complement
, Article Linear Algebra and Its Applications ; Volume 555 , 2018 , Pages 157-162 ; 00243795 (ISSN) ; Akbari, S ; Moghaddamzadeh, M. J ; Mohar, B ; Sharif University of Technology
Elsevier Inc
2018
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ2(G)+λ2(G‾)≥1, where G‾ is the complement of G. In this paper, it is shown that max{λ2(G),λ2(G‾)}≥[Formula presented]. © 2018 Elsevier Inc
NLOS identification in range-based source localization: statistical approach
, Article IEEE Sensors Journal ; Volume 18, Issue 9 , 1 May , 2018 , Pages 3745-3751 ; 1530437X (ISSN) ; Behnia, F ; Amiri, R ; Marvasti, F ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
Least squares estimation is a widely-used technique for range-based source localization, which obtains the most probable position of mobile station. These methods cannot provide desirable accuracy in the case with a non line of sight (NLOS) path between mobile station and base stations. To circumvent this drawback, many algorithms have been proposed to identify and mitigate this error; however, they have a large run-time overhead. On the other hand, new positioning systems utilize a large set of base stations, and a practical algorithm should be fast enough to deal with them. In this paper, we propose a novel algorithm based on subspace method to identify and eliminate the NLOS error....
Numerical modeling of shear band propagation in porous plastic dilatant materials by XFEM
, Article Theoretical and Applied Fracture Mechanics ; Volume 95 , 2018 , Pages 164-176 ; 01678442 (ISSN) ; Liu, P ; Sharif University of Technology
Elsevier B.V
2018
Abstract
This paper studies mixed-mode shear band propagation behaviors in porous plastic dilatant materials by the extended finite element method (XFEM). The Drucker-Prager elastoplastic model is combined with the strong discontinuity method to simulate the dilatant shear band. First, the dissipative nature of the localized area with displacement jump is integrated into the constitutive model by introducing a cohesive law. A new contribution lies that the yielding function is modified in the localized region to calculate the cohesive traction within the framework of the XFEM. The shear band propagation direction is determined by the singularity of the acoustic tensor and the corresponding...
Complex modal analysis and coupled electromechanical simulation of energy harvesting piezoelectric laminated beams
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; 2018 ; 09544062 (ISSN) ; Ahmadian, M. T ; Zohoor, H ; Sharif University of Technology
SAGE Publications Ltd
2018
Abstract
In this paper, coupled electromechanical behavior of a vibrational energy harvesting system composed of a unimorph piezoelectric laminated beam with a large attached tip mass is investigated. To achieve this goal, first the electromechanically coupled partial differential equations governing the lateral displacement and output voltage of the harvester are extracted through exploiting the Hamilton’s principle. Considering vibration damping due to mechanical to electrical energy conversion, a complex modal analysis is performed to extract the complex eigenfrequencies and eigenfunctions of the system. Furthermore, an exact analytical solution is presented for the system response to the harmonic...
Robust stability analysis of uncertain multiorder fractional systems: young and Jensen inequalities approach
, Article International Journal of Robust and Nonlinear Control ; Volume 28, Issue 4 , March , 2018 , Pages 1127-1144 ; 10498923 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
John Wiley and Sons Ltd
2018
Abstract
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
Rewirings based on the eigenvectors of the laplacian matrix for enhancing synchronizability of dynamical networks
, Article 2009 7th IEEE International Conference on Industrial Informatics, INDIN 2009, Cardiff, 23 June 2009 through 26 June 2009 ; 2009 , Pages 588-593 ; 19354576 (ISSN); 9781424437603 (ISBN) ; Ajdari Rad, A ; Sharif University of Technology
2009
Abstract
Synchronizability of dynamical networks can be defined as the ease by which the network synchronizes its activity. We propose a method for enhancing the synchronizability of dynamical networks by efficient rewirings. The method is based on the eigenvectors corresponding to the second smallest and the largest eigenvalue of the Laplacian matrix and a modified version of the simulated annealing approach is used to perform the optimization task. Starting from a simple network, i.e. an undirected and unweighted network, and at each step, an edge is selected for disconnection and two non-adjacent nodes for creating at edge in between. The effectiveness of the algorithm is tested on artificially...
Aeroelastic analysis of helicopter rotor blade in hover using an efficient reduced-order aerodynamic model
, Article Journal of Fluids and Structures ; Volume 25, Issue 8 , 2009 , Pages 1243-1257 ; 08899746 (ISSN) ; Salehzadeh Noubari, A ; Behbahani Nejad, M ; Haddadpour, H ; Sharif University of Technology
2009
Abstract
This paper presents a coupled flap-lag-torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton-Raphson method. Numerical results comprising steady equilibrium...
True damping and frequency prediction for aeroelastic systems: The PP method
, Article Journal of Fluids and Structures ; Volume 25, Issue 7 , 2009 , Pages 1177-1188 ; 08899746 (ISSN) ; Firouz Abadi, R. D ; Sharif University of Technology
2009
Abstract
This paper presents a numerical scheme for stability analysis of the aeroelastic systems in the Laplace domain. The proposed technique, which is called the PP method, is proposed for when the aerodynamic model is represented in the Laplace domain and includes complicated transcendental expressions in terms of the Laplace variable. This method utilizes a matrix iterative procedure to find the eigenvalues of the system and generalizes the other methods such as the P and PK methods for prediction of the flutter conditions. The major advantage of this technique over the other approximate methods is true prediction of subcritical damping and frequency values of the aeroelastic modes. To examine...
Optimal and robust waveform design for MIMO radars
, Article 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, 19 April 2009 through 24 April 2009 ; 2009 , Pages 2085-2088 ; 15206149 (ISSN); 9781424423545 (ISBN) ; Behnia, F ; Institute of Electrical and Electronics Engineers; Signal Processing Society ; Sharif University of Technology
2009
Abstract
Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise, here we extend the results to the case where signal-dependent noise, clutter, is also present and then we find the optimum waveform for several estimators differing in the assumptions on the given statistics. Computing the optimal waveforms for MMSE estimator leads to the Semi-definite programming (SDP) problem. Finding the optimal transmit signals for CSLS estimator results in a minimax eigenvalue problem. Finally it is shown that equal power waveforms are the best transmit signals for the SLS estimator....