Search results for: eigenvalue method

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Abubakar Sadiq Mensah

Abstract:

The Knowledge of the population growth of a nation is paramount to national planning. The population of a place is studied and a model developed over a period of time, Matrices is used to form model for population growth. The eigenvalue ƛ of the matrix A and its corresponding eigenvector X is such that AX = ƛX is calculated. The stable age distribution of the population is obtained using the eigenvalue and the characteristic polynomial. Hence, estimation could be made using eigenvalues and eigenvectors.

Keywords: eigenvalues, eigenvectors, population, growth/stability

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

Abstract:

The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm–Liouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

Abstract:

We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

Abstract:

This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: Mouhamadou Dosso

Abstract:

This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.

Keywords: spectral dichotomy method, spectral projector, eigensubspaces, eigenvalue

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Authors: Rashid Ahmed , John N. Avaritsiotis

Abstract:

Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural networks are presented. First, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Second, minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a Minor Component Analysis (MCA(R)) learning algorithm to enhance the convergence, where a convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Preliminary results will be furnished to illustrate the convergences results achieved.

Keywords: Direction of Arrival, neural networks, Principle Component Analysis, Minor Component Analysis

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

Abstract:

A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: eigenvalue analysis, microgrid, modal analysis, voltage stability

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Authors: Shaowei Sun

Abstract:

Let G be a graph with vertex set V(G)={v_1,v_2,...,v_n} and edge set E(G). For any vertex v belong to V(G), let d_v denote the degree of v. The normalized Laplacian matrix of the graph G is the matrix where the non-diagonal (i,j)-th entry is -1/(d_id_j) when vertex i is adjacent to vertex j and 0 when they are not adjacent, and the diagonal (i,i)-th entry is the di. In this paper, we discuss some bounds on the largest and the second smallest normalized Laplacian eigenvalue of trees and graphs. As following, we found some new bounds on the second smallest normalized Laplacian eigenvalue of tree T in terms of graph parameters. Moreover, we use Sage to give some conjectures on the second largest and the third smallest normalized eigenvalues of graph.

Keywords: graph, normalized Laplacian eigenvalues, normalized Laplacian matrix, tree

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Authors: Burak Yildirim, Muhsin Tunay Gencoglu

Abstract:

This publication shows the effects of Microgrid (MG) integration on the power systems oscillating stability. Generated MG model power systems were applied to the IEEE 14 bus test system which is widely used in stability studies. Stability studies were carried out with the help of eigenvalue analysis over linearized system models. In addition, Hopf bifurcation point detection was performed to show the effect of MGs on the system loadability margin. In the study results, it is seen that MGs affect system stability positively by increasing system loadability margin and has a damper effect on the critical modes of the system and the electromechanical local modes, but they make the damping amount of the electromechanical interarea modes reduce.

Keywords: Eigenvalue analysis, microgrid, Hopf bifurcation, oscillatory stability

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Authors: Zhuoran Li, Guan Qin

Abstract:

A robust and efficient compositional equilibrium characterization model for hydrate-containing systems is required, especially for time-critical simulations such as subsea pipeline flow assurance analysis, compositional simulation in hydrate reservoirs etc. A multiphase flash calculation framework, which combines Gibbs energy minimization function and cubic plus association (CPA) EoS, is developed to describe the highly non-ideal phase behavior of hydrate-containing systems. A non-iterative eigenvalue problem-solving approach for the trust-region sub-problem is selected to guarantee efficiency. The developed flash model is based on the state-of-the-art objective function proposed by Michelsen to minimize the Gibbs energy of the multiphase system. It is conceivable that a hydrate-containing system always contains polar components (such as water and hydrate inhibitors), introducing hydrogen bonds to influence phase behavior. Thus, the cubic plus associating (CPA) EoS is utilized to compute the thermodynamic parameters. The solid solution theory proposed by van der Waals and Platteeuw is applied to represent hydrate phase parameters. The trust-region method combined with the trust-region sub-problem non-iterative eigenvalue problem-solving approach is utilized to ensure fast convergence. The developed multiphase flash model's accuracy performance is validated by three available models (one published and two commercial models). Hundreds of published hydrate-containing system equilibrium experimental data are collected to act as the standard group for the accuracy test. The accuracy comparing results show that our model has superior performances over two models and comparable calculation accuracy to CSMGem. Efficiency performance test also has been carried out. Because the trust-region method can determine the optimization step's direction and size simultaneously, fast solution progress can be obtained. The comparison results show that less iteration number is needed to optimize the objective function by utilizing trust-region methods than applying line search methods. The non-iterative eigenvalue problem approach also performs faster computation speed than the conventional iterative solving algorithm for the trust-region sub-problem, further improving the calculation efficiency. A new thermodynamic framework of the multiphase flash model for the hydrate-containing system has been constructed in this work. Sensitive analysis and numerical experiments have been carried out to prove the accuracy and efficiency of this model. Furthermore, based on the current thermodynamic model in the oil and gas industry, implementing this model is simple.

Keywords: equation of state, hydrates, multiphase equilibrium, trust-region method

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Authors: Sameena Tarannum, S. Pranesh

Abstract:

The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: gravity modulation, Oldroyd-b liquid, triple diffusive convection, venezian approach

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Authors: Alfi Y. Zakiyyah, Hanni Garminia, M. Salman, A. N. Irawati

Abstract:

In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.

Keywords: connectivity, graph, hypergraph, Laplacian matrix

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Authors: Yaping Zhao

Abstract:

In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Zia R. Tahir, P. Mandal

Abstract:

This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0°/+45°/-45°/0°] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

Keywords: CFRP composite cylindrical shell, asymmetric meshing technique, primary buckling, secondary buckling, linear eigenvalue analysis, non-linear riks analysis

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

Abstract:

In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: N. F. M. Mokhtar, N. Z. A. Hamid

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This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

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Authors: Falek Kamel

Abstract:

Various approaches are usually used in the dynamic analysis of beams vibrating transversally. For this, numerical methods allowing the solving of the general eigenvalue problem are utilized. The equilibrium equations describe the movement resulting from the solution of a fourth-order differential equation. Our investigation is based on the finite element method. The findings of these investigations are the vibration frequencies obtained by the Jacobi method. Two types of the elementary mass matrix are considered, representing a uniform distribution of the mass along with the element and concentrated ones located at fixed points whose number is increased progressively separated by equal distances at each evaluation stage. The studied beams have different boundary constraints representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculus stage is to obtain the lowest number of beam parts that gives a frequency comparable to that issued from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are used for the second type of mass representation in the same manner.

Keywords: structural elements, beams vibrating, dynamic analysis, finite element method, Jacobi method

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Authors: Eric D. Olson

Abstract:

The lesbian/gay/bisexual/transgender/queer/questioning tourist (LGBTQ+) travels more frequently, spends more money on travel, and is more likely to travel internationally compared to their straight/heterosexual counterparts. For Vietnam, this represents a huge opportunity to increase international tourism, considering social advancements and recognition of the LGBTQ+ have greatly increased in the past few years in Vietnam. For example, Vietnam’s Health Ministry confirmed in 2022 that same-sex attraction and being transgender is not a mental health condition. A robust hospitality ecosystem of LGBTQ+ tourism suppliers already exists in Vietnam catering to LGBTQ+ tourists (e.g., Gay Hanoi Tours, VietPride). Vietnam is a safe and welcoming destination with incredible nature, cosmopolitan cities, and friendly people; however, there is a dearth of academic and industry research that has examined how LGBTQ+ international tourists perceive Vietnam as an LGBTQ+ friendly destination. To rectify this gap, this research examines Vietnam as an LGBTQ+ destination in order to provide government officials, destination marketers, and industry practitioners with insight into this increasingly visible tourist market segment. A self-administered survey instrument was administered to n=375 international LGBTQ+ tourists to examine their perceptions of Vietnam. A factor analysis found three categories of LGBTQ+ factors of visitation to Vietnam: safety and security (Eigenvalue = 4.12, variance = 32.45, α = .82); LGBTQ+ attractions (Eigenvalue = 3.65 variance = 24.23, α = .75); and friendly interactions (Eigenvalue = 3.71, variance = 10.45, α = .96). Multiple regression was used to examine LGBTQ+ visitation factors and intention to visit Vietnam, F=12.20 (2, 127), p < .001, R2 = .56. Safety and security (β = 0.42, p < .001), LGBTQ+ attractions (β = 0.61, p < .001) and friendly interactions (β = 0.42, p < .001) are predictors to visit Vietnam. Results are consistent with previous research that highlight safety/security is of utmost importance to the community when traveling. Attractions, such as LGBTQ+ tours, suppliers, and festivals can also be used as a pull factor in encouraging tourism. Implications/limitations will be discussed.

Keywords: tourism, LGBTQ, vietnam, regression

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: M. M. Qasaymeh, M. A. Khodeir

Abstract:

Subspace channel estimation methods have been studied widely. It depends on subspace decomposition of the covariance matrix to separate signal subspace from noise subspace. The decomposition normally is done by either Eigenvalue Decomposition (EVD) or Singular Value Decomposition (SVD) of the Auto-Correlation matrix (ACM). However, the subspace decomposition process is computationally expensive. In this paper, the multipath channel estimation problem for a Slow Frequency Hopping (SFH) system using noise space based method is considered. An efficient method to estimate multipath the time delays basically is proposed, by applying MUltiple Signal Classification (MUSIC) algorithm which used the null space extracted by the Rank Revealing LU factorization (RRLU). The RRLU provides accurate information about the rank and the numerical null space which make it a valuable tool in numerical linear algebra. The proposed novel method decreases the computational complexity approximately to the half compared with RRQR methods keeping the same performance. Computer simulations are also included to demonstrate the effectiveness of the proposed scheme.

Keywords: frequency hopping, channel model, time delay estimation, RRLU, RRQR, MUSIC, LS-ESPRIT

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Authors: Falek Kamel

Abstract:

Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.

Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory

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Authors: N. H. Z. Abidin, N. F. M. Mokhtar, S. S. A. Gani

Abstract:

The influence of diffusion of the thermal or known as Soret effect in a heated Binary fluid model with Coriolis force is investigated theoretically. The linear stability analysis is used, and the eigenvalue is obtained using the Galerkin method. The impact of the Soret and Coriolis force on the onset of stationary convection in a system is analysed with respect to various Binary fluid parameters and presented graphically. It is found that an increase of the Soret values, destabilize the Binary fluid layer system. However, elevating the values of the Coriolis force helps to lag the onset of convection in a system.

Keywords: Benard convection, binary fluid, Coriolis, Soret

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Authors: Houari Boumediene University of Science, Technology.

Abstract:

"Various methods are typically used in the dynamic analysis of transversely vibrating beams. To achieve this, numerical methods are used to solve the general eigenvalue problem. The equations of equilibrium, which describe the motion, are derived from a fourth-order differential equation. Our study is based on the finite element method, and the results of the investigation are the vibration frequencies obtained using the Jacobi method. Two types of elementary mass matrices are considered: one representing a uniform distribution of mass along the element and the other consisting of concentrated masses located at fixed points whose number increases progressively with equal distances at each evaluation stage. The beams studied have different boundary constraints, representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculation stage involves determining the lowest number of beam parts that gives a frequency comparable to that obtained from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are repeated for the second type of mass representation in the same manner."

Keywords: finite element method, bernouilli eulertheory, structural analysis, vibration analysis, rayleigh quotient

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Authors: Theddeus Tochukwu Akano, Omotayo Abayomi Fakinlede

Abstract:

Proper understanding of the behavior of compliant mechanisms use by athletes is important in order to avoid catastrophic failure. Such compliant mechanisms like the flex-run require the knowledge of their dynamic response and deformation behavior under quickly varying loads. The modeling of finite deformations of the compliant athletic system is described by Neo-Hookean model under contact-impact conditions. The dynamic impact-contact governing equations for both the target and impactor are derived based on the updated Lagrangian approach. A method where contactor and target are considered as a united body is applied in the formulation of the principle of virtual work for the bodies. In this paper, methods of continuum mechanics and nonlinear finite element method were deployed to develop a model that could capture the behavior of the compliant athletic system under quickly varying loads. A hybrid system of symbolic algebra (AceGEN) and a compiled back end (AceFEM) were employed, leveraging both ease of use and computational efficiency. The simulated results reveal the effect of the various contact-impact conditions on the deformation behavior of the impacting compliant mechanism.

Keywords: eigenvalue problems, finite element method, robin boundary condition, sturm-liouville problem

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

Abstract:

In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: Amir R. Askari, Masoud Tahani

Abstract:

The objective of the present paper is to investigate the effect of size on the vibrational behavior of fully clamped rectangular micro-plates based on the modified couple stress theory (MCST). To this end, a size-dependent Kirchhoff plate model is considered and the equation of motion which accounts for the effect of residual and couple stress components is derived using the Hamilton's principle. The eigenvalue problem associated with the free vibrations of fully clamped micro-plates is extracted and solved analytically using the extended Kantorovich method (EKM). The present findings are compared and validated by available results in the literature and an excellent agreement between them is observed. A parametric study is also conducted to show the significant effects of couple stress components on natural frequencies of fully clamped micro-plates. It is found that the ratio of MCST natural frequencies to those obtained by the classical theory (CT) only depends on the Poisson's ratio of the plate and is totally independent of plate's aspect ratio for cases with no residual stresses.

Keywords: vibrational analysis, modified couple stress theory, fully clamped rectangular micro-plates, extended Kantorovich method.

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

Abstract:

This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: axial deformation, free vibration, Galerkin finite element method, large amplitude, variational method

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Authors: Amares Chattopadhyay, Akanksha Srivastava

Abstract:

A unified approach to study the reflection of a plane wave in three-dimensional model comprised of the triclinic viscoelastic medium. The phase velocities of reflected qP, qSV and qSH wave have been calculated for the concerned medium by using the eigenvalue approach. The generalized method has been implemented to compute the complex form of amplitude ratios. Further, we discussed the nature of reflection coefficients of qP, qSV and qSH wave. The viscoelastic parameter, polar angle and azimuthal angle are found to be strongly influenced by amplitude ratios. The research article is particularly focused to study the effect of viscoelasticity associated with highly anisotropic media which exhibits the notable information about the reflection coefficients of qP, qSV, and qSH wave. The outcomes may further useful to the better exploration of all types of hydrocarbon reservoir and advancement in the field of reflection seismology.

Keywords: amplitude ratios, three dimensional, triclinic, viscoelastic

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

Abstract:

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: eigenvalues/eigenvectors, latent values/vectors, matrix fraction description, state space description

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