Sharif Digital Repository

Various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional (2-D) shear building structural models for a given set of vibratory frequencies. The suggested methods are based on the specific characteristics of the Jacobi matrices, i.e., symmetric, tri-diagonal and semi-positive definite matrices. However, in case of three dimensional (3-D) structural models, those methods are no longer applicable, since their stiffness matrices are not tri-diagonal. In this paper the inverse problem for a special class of vibratory structural systems, i.e., 3-D shear building models, is investigated. A practical algorithm is proposed for solving the inverse... 

This study presents a developed successive Boundary Element Method to determine the symmetric and antisymmetric sloshing natural frequencies and mode shapes for multi baffled axisymmetric containers with arbitrary geometries. The developed fluid model is based on the Laplace equation and Green's theorem. The governing equations of fluid dynamic and free surface boundary condition are also applied to proposed model. A zoning method is presented to model arbitrary arrangement of baffles in multi baffled axisymmetric tanks. The influence of each zone on neighboring zones is applied by introducing interface influence matrix which correlates the velocity potential of interfaces to their flux. By... 

In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with... 

In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with... 

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass.... 

In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending–torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the... 

In this paper, we consider the network coding in networks with broadcast channels (called hypernetworks) as the first step for applying network coding to wireless networks. We first prove a Max-Flow Min-Cut theorem for such networks. While we propose an algorithm to achieve this bound, we will introduce new definitions and provide sufficient tools to extend many of the theorems stated for flows in wireline networks to the case of hypernetworks. As an example, we will extend the Max-Flow Min-Cut condition for feasibility of the point-to-point connection in wireline networks to the case of hypernetworks. Then, we will extend the algebraic approach of Koetter and Medard in [3] to the... 

Fourier-based modal methods are among the most significant tools for accurate numerical analysis of grating structures. However, they mostly lead to time consuming and memory hungry eigenvalue problems, particularly when large dielectric constants or high contrasts are involved. We have found an asymptotic semi-empirical relationship for the propagation constants of a lamellar grating, obtained from Fourier-based modal methods. Hence, given any truncation order, it is possible to estimate propagation constants without having to solve the eigenvalue equation. We observed propagation constants only depend on permittivities, filling factors, and the unit cell size, while the dependence on the... 

Fourier-based modal methods are among the most effective numerical tools for the accurate analysis of crossed gratings. However, leading to computationally expensive eigenvalue equations significantly restricts their applicability, particularly when large truncation orders are required. The resultant eigenvalues are the longitudinal propagation constants of the grating and play a key role in applying the boundary conditions, as well as in the convergence and stability analyses. This paper aims to propose simple techniques for the fast estimation of propagation constants in crossed gratings, predominantly with no need to solve an eigenvalue equation. In particular, we show that for regular... 

This paper is concerned with the stability of linear time-invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when an encoder and a decoder are unaware of the control signal. This assumption results in co-designing the encoder, decoder and controller. The encoder, decoder, controller and conditions relating transmission rate to packet erasure probability and eigenvalues of the system matrix A are presented for almost sure asymptotic stability of linear time-invariant dynamic systems over the packet erasure channel with feedback acknowledgment. When the eigenvalues of the system matrix A are real valued, it is shown that the obtained condition for... 

Stability analysis of a horizontal cantilevered pipe conveying fluid with an inclined terminal nozzle is considered in this paper. The pipe is modelled as a cantilevered Euler-Bernoulli beam, and the flow-induced inertia, Coriolis and centrifugal forces along the pipe as well as the follower force induced by the jet-flow are taken into account. The governing equations of the coupled bending-torsional vibrations of the pipe are obtained using extended Hamilton's principle and are then discretized via the Galerkin method. The resulting eigenvalue problem is then solved, and several cases are examined to determine the effect of nozzle inclination angle, nozzle aspect ratio, mass ratio and... 

In this paper, a fluid-structure interaction model for stability analysis of shells conveying fluid is developed. This model is developed for shells of arbitrary geometry and structure and is based on incompressible potential flow. The boundary element method is applied to model the potential flow. The fluid dynamics model is derived by using an inflow/outflow model along with the impermeability condition at the fluid-shell interface. This model is applied to obtain the flow modes and eigenvalues, which are used for the modal representation of the flow field in the shell. Based on the mode shapes and natural frequencies of the shell obtained from an FEM model, the modal analysis technique is... 

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

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... 

Recommender systems have become an important issue in network science. Collaborative filtering and its variants are the most widely used approaches for building recommender systems, which have received great attention in both academia and industry. In this paper, we studied the relationship between recommender systems and connectivity of users-items bipartite network. This results in a novel recommendation algorithm. In our method recommended items are selected based on the eigenvector corresponding to the algebraic connectivity of the graph - the second smallest eigenvalue of the Laplacian matrix. Since recommending an item to a user equals to adding a new link to the users-items bipartite... 

In this paper a novel supplementary subsynchronous damping controller (SSDC) is proposed for the STATic synchronous COMpensator (STATCOM) which is capable of damping out subsynchronous oscillations in power system with series compensated transmission lines. An auxiliary subsynchronous damping controller (SSDC) for a STATCOM using the generator rotor speed deviation signal as the stabilizing signal has been designed to damp subsynchronous oscillations. Eigenvalue analysis and transient simulations of detailed nonlinear system are considered to investigate the performance of the controller. Robustness of the controller has been analyzed by facing the system with disturbances leading to... 

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b (G). A known lower bound on b (G) states that b (G) ≥max {p (G), q (G)}, where p (G) and q (G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b (G) = max {p (G), q (G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness of graphs with at most one cycle and products of some families of graphs. Among the other results, we show that Pm ∨ Pn, Cm ∨ Pn for m ≡ 2, 3 (mod 4) and Qn when n is odd are eigensharp. We obtain some results on... 

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... 

In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ϵ turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which... 

In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ϵ turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which...