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#### Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core

, Article Composite Structures ; Volume 255 , 2021 ; 02638223 (ISSN) ; Asgari, M ; Haddadpour, H ; Sharif University of Technology
Elsevier Ltd
2021

Abstract

The free linear vibration of an adaptive sandwich beam consisting of a frequency and field-dependent magnetorheological fluid core and an axially functionally graded constraining layer is investigated. The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. The Rayleigh-Ritz method is used to derive the frequency-dependent eigenvalue problem through the kinetic and strain energy expressions of the sandwich beam. In order to deal with the frequency dependency of the core, the approached complex eigenmodes method is implemented. The validity of the formulation and solution method is confirmed through comparison...

#### Theoretical and experimental analysis of the free vibrations of a shell made of n cone segments joined together

, Article Thin-Walled Structures ; Volume 108 , 2016 , Pages 416-427 ; 02638231 (ISSN) ; Saadat Foumani, M ; Navazi, H. M ; Sharif University of Technology
Elsevier Ltd

Abstract

This paper investigates the free vibrations of a shell made of n cone segments joined together. The governing equations of the conical shell were obtained by applying the Sanders shell theory and the Hamilton principle. Then, these governing equations are solved by using the power series method and considering a displacement field which is harmonic function about the time and the circumferential coordinate. Using the boundary conditions of the two ends of the shell and the continuity conditions at the interface section of shell segments, and solving the eigenvalue problem, the natural frequencies and the mode shapes are obtained. Very good agreements exist between the analytical results of...

#### 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

#### On the largest eigenvalue of signed unicyclic graphs

, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 145-162 ; 00243795 (ISSN) ; Belardo, F ; Heydari, F ; Maghasedi, M ; Souri, M ; Sharif University of Technology
Elsevier Inc
2019

Abstract

Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3. © 2019

#### On the minimum energy of regular graphs

, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 51-71 ; 00243795 (ISSN) ; Akbari, S ; Ghasemian, E ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2019

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G)≥n. Here, we improve this result by showing that if G is a connected subcubic graph of order n≥8, then E(G)≥1.01n. Also, we prove that if G is a traceable subcubic graph of order n≥8, then E(G)>1.1n. Let G be a connected cubic graph of order n≥8, it is shown that E(G)>n+2. It was proved that if G is a connected cubic graph of order n, then E(G)≤1.65n. Also, in this paper we would like to present the best lower bound for the energy of a connected cubic graph. We introduce an infinite family of connected cubic graphs whose for...

#### Some results on the Laplacian spread conjecture

, Article Linear Algebra and Its Applications ; Volume 574 , 2019 , Pages 22-29 ; 00243795 (ISSN) ; Akbari, S ; Sharif University of Technology
Elsevier Inc
2019

Abstract

For a graph G of order n, let λ 2 (G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ 2 (G)+λ 2 (G‾)≥1, where G‾ is the complement of G. For any x∈R n , let ∇ x ∈R (n2) be the vector whose {i,j}-th entry is |x i −x j |. In this paper, we show the aforementioned conjecture is equivalent to prove that every two orthonormal vectors f,g∈R n with zero mean satisfy ‖∇ f −∇ g ‖ 2 ≥2. In this article, it is shown that for the validity of the conjecture it suffices to prove that the conjecture holds for all permutation graphs. © 2019 Elsevier Inc

#### Some lower bounds for the energy of graphs

, Article Linear Algebra and Its Applications ; Volume 591 , 2020 , Pages 205-214 ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Sharif University of Technology
Elsevier Inc
2020

Abstract

The singular values of a matrix A are defined as the square roots of the eigenvalues of A⁎A, and the energy of A denoted by E(A) is the sum of its singular values. The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In this paper, we prove that if A is a Hermitian matrix with the block form A=(BDD⁎C), then E(A)≥2E(D). Also, we show that if G is a graph and H is a spanning subgraph of G such that E(H) is an edge cut of G, then E(H)≤E(G), i.e., adding any number of edges to each part of a bipartite graph does not decrease its energy. Let G be a connected graph of order n and size m with the adjacency matrix A. It is well-known...

#### Trees with a large Laplacian eigenvalue multiplicity

, Article Linear Algebra and Its Applications ; Volume 586 , 2020 , Pages 262-273 ; van Dam, E. R ; Fakharan, M. H ; Sharif University of Technology
Elsevier Inc
2020

Abstract

In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than 1 are simple and also the multiplicity of Laplacian eigenvalue 1 has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order n that have a multiplicity that is close to the upper bound [Formula presented], and emphasize the particular role of the algebraic connectivity. © 2019 Elsevier Inc

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; 2020 ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
Elsevier Inc
2020

Abstract

A signed graph Gσ is an ordered pair (V(G),E(G)), where V(G) and E(G) are the set of vertices and edges of G, respectively, along with a map σ that signs every edge of G with +1 or −1. An eigenvalue of the associated adjacency matrix of Gσ, denoted by A(Gσ), is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. We conjectured that for every graph G≠K2,K4{e}, there is a switching σ such that all eigenvalues of Gσ are main. We show that this conjecture holds for every Cayley graphs, distance-regular graphs, vertex and edge-transitive graphs as well as double stars and paths. © 2020 Elsevier Inc

#### Hypoenergetic and nonhypoenergetic digraphs

, Article Linear Algebra and Its Applications ; Volume 618 , 2021 , Pages 129-143 ; 00243795 (ISSN) ; Das, K. C ; Khalashi Ghezelahmad, S ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2021

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. This concept was extended by Nikiforov to arbitrary complex matrices. Recall that the trace norm of a digraph D is defined as, N(D)=∑i=1nσi, where σ1≥⋯≥σn are the singular values of the adjacency matrix of D. In this paper we would like to present some lower and upper bounds for N(D). For any digraph D it is proved that N(D)≥rank(D) and the equality holds if and only if D is a disjoint union of directed cycles and directed paths. Finally, we present a lower bound on σ1 and N(D) in terms of the size of digraph D. © 2021 Elsevier Inc

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; Volume 614 , 2021 , Pages 270-280 ; 00243795 (ISSN) ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
Elsevier Inc
2021

Abstract

A signed graph Gσ is an ordered pair (V(G),E(G)), where V(G) and E(G) are the set of vertices and edges of G, respectively, along with a map σ that signs every edge of G with +1 or −1. An eigenvalue of the associated adjacency matrix of Gσ, denoted by A(Gσ), is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. We conjectured that for every graph G≠K2,K4{e}, there is a switching σ such that all eigenvalues of Gσ are main. We show that this conjecture holds for every Cayley graphs, distance-regular graphs, vertex and edge-transitive graphs as well as double stars and paths. © 2020 Elsevier Inc

#### Hypoenergetic and nonhypoenergetic digraphs

, Article Linear Algebra and Its Applications ; Volume 618 , 2021 , Pages 129-143 ; 00243795 (ISSN) ; Das, K. C ; Khalashi Ghezelahmad, S ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2021

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. This concept was extended by Nikiforov to arbitrary complex matrices. Recall that the trace norm of a digraph D is defined as, N(D)=∑i=1nσi, where σ1≥⋯≥σn are the singular values of the adjacency matrix of D. In this paper we would like to present some lower and upper bounds for N(D). For any digraph D it is proved that N(D)≥rank(D) and the equality holds if and only if D is a disjoint union of directed cycles and directed paths. Finally, we present a lower bound on σ1 and N(D) in terms of the size of digraph D. © 2021 Elsevier Inc

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; Volume 614 , 2021 , Pages 270-280 ; 00243795 (ISSN) ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
Elsevier Inc
2021

Abstract

A signed graph Gσ is an ordered pair (V(G),E(G)), where V(G) and E(G) are the set of vertices and edges of G, respectively, along with a map σ that signs every edge of G with +1 or −1. An eigenvalue of the associated adjacency matrix of Gσ, denoted by A(Gσ), is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. We conjectured that for every graph G≠K2,K4{e}, there is a switching σ such that all eigenvalues of Gσ are main. We show that this conjecture holds for every Cayley graphs, distance-regular graphs, vertex and edge-transitive graphs as well as double stars and paths. © 2020 Elsevier Inc

#### Linearization error in synchronization of Kuramoto oscillators

, Article Applied Mathematics and Computation ; Volume 411 , December , 2021 ; 00963003 (ISSN) ; Baharifard, F ; Hesaam, B ; Zarei, M ; Sarbazi Azad, H ; Sharif University of Technology
Elsevier Inc
2021

Abstract

Synchronization among a set of networked nodes has attracted much attention in different fields. This paper thoroughly investigates linear formulation of the Kuramoto model, with and without frustration, for an arbitrarily weighted undirected network where all nodes may have different intrinsic frequencies. We develop a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks. We mathematically prove that the eigenvector corresponding to the largest eigenvalue of the network's Laplacian matrix is enough for examining synchrony alignment and that the functionality of this vector depends on the corresponding eigenvalue. Moreover, we prove...

#### 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...

#### UWB orthogonal pulse design using Sturm–Liouville boundary value problem

, Article Signal Processing ; Volume 159 , 2019 , Pages 147-158 ; 01651684 (ISSN) ; Mohajerin Esfahani, P ; Ghavami, M ; Marvasti, F ; Sharif University of Technology
Elsevier B.V
2019

Abstract

The problem of designing UWB pulses which meet specific spectrum requirements is usually treated by filtering common pulses such as Gaussian doublets, modified Hermite polynomials and wavelets. When there is the need to have a number of orthogonal pulses (e.g., in a multiuser scenario), a naive approach is to filter all the members of an orthogonal set, which is likely to destroy their orthogonality property. In this paper, we study the design of a set of pulses that simultaneously satisfy the orthogonality property and spectrum requirements. Our design is based on the eigenfunctions of Sturm–Liouville boundary value problems. Indeed, we introduce Sturm–Liouville differential equations for...

#### Estimation and stability over AWGN channel in the presence of fading, noisy feedback channel and different sample rates

, Article Systems and Control Letters ; Volume 123 , 2019 , Pages 75-84 ; 01676911 (ISSN) ; https://www.sciencedirect.com/science/article/abs/pii/S0167691118301993 ; Farhadi, A ; Khalaj, B. H ; Motahari, A. S ; Sharif University of Technology
Elsevier B.V
2019

Abstract

This paper is concerned with estimation and stability of control systems over communication links subject to limited capacity, power constraint, fading, noisy feedback, and different transmission rate rather than system sampling rate. A key issue addressed in this paper is that in the presence of noisy feedback associated with channel, which models transmission of finite number of bits over such links as is the case in most practical scenarios, the well-known eigenvalues rate condition is still a tight bound for stability. Based on an information theoretic analysis, necessary conditions are derived for stability of discrete-time linear control systems via the distant controller in the mean...

#### Estimation and stability over AWGN channel in the presence of fading, noisy feedback channel and different sample rates

, Article Systems and Control Letters ; Volume 123 , 2019 , Pages 75-84 ; 01676911 (ISSN) ; Farhadi, A ; Khalaj, B. H ; Seyed Motahari, A ; Sharif University of Technology
Elsevier B.V
2019

Abstract

This paper is concerned with estimation and stability of control systems over communication links subject to limited capacity, power constraint, fading, noisy feedback, and different transmission rate rather than system sampling rate. A key issue addressed in this paper is that in the presence of noisy feedback associated with channel, which models transmission of finite number of bits over such links as is the case in most practical scenarios, the well-known eigenvalues rate condition is still a tight bound for stability. Based on an information theoretic analysis, necessary conditions are derived for stability of discrete-time linear control systems via the distant controller in the mean...

#### Investigation of the effect of turbulence intensity and nozzle exit boundary layer thickness on stability pattern of subsonic jet

, Article Mechanics and Industry ; Volume 20, Issue 1 , 2019 ; 22577777 (ISSN) ; Arablu, S ; Afshin, H ; Farhanieh, B ; Sharif University of Technology
EDP Sciences
2019

Abstract

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...

#### Investigation of the effect of turbulence intensity and nozzle exit boundary layer thickness on stability pattern of subsonic jet

, Article Mechanics and Industry ; Volume 20, Issue 1 , 2019 ; 22577777 (ISSN) ; Arablu, S ; Afshin, H ; Farhanieh, B ; Sharif University of Technology
EDP Sciences
2019

Abstract

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...