• Title, Summary, Keyword: Sylvester

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Flexural Free Vibration Analysis of Axisymmetric Annular Plates Using Sylvester-Transfer Stiffness Coefficient Method (실베스터-전달강성계수법을 이용한 축대칭 환원판의 굽힘 자유진동 해석)

  • Choi, Myung-Soo;Kondou, Takahiro;Byun, Jung-Hwan;Yeo, Dong-Jun
    • Journal of Power System Engineering
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    • v.19 no.6
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    • pp.60-67
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    • 2015
  • While designing and operating machines, it is very important to understand the dynamic characteristic of the machines. Authors developed the Sylvester-transfer stiffness coefficient method in order to analyze effectively the free vibration of machines or structures. The Sylvester-transfer stiffness coefficient method was derived from the combination of the Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the authors formulate the computational algorithm for flexural free vibration analysis of axisymmetric annular plate using the Sylvester-transfer stiffness coefficient method. To confirm the usefulness of the Sylvester-transfer stiffness coefficient method, the natural frequencies and modes for two computational models computed using the Sylvester-transfer stiffness coefficient method are compared with those computed using the exact solution and the finite element method.

SOLVABILITY OF SYLVESTER OPERATOR EQUATION WITH BOUNDED SUBNORMAL OPERATORS IN HILBERT SPACES

  • Bekkar, Lourabi Hariz;Mansour, Abdelouahab
    • Korean Journal of Mathematics
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    • v.27 no.2
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    • pp.515-523
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    • 2019
  • The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.

Free Vibration Analysis of Axisymmetric Cylindrical Shell by Sylvester-Transfer Stiffness Coefficient Method (실베스터-전달강성계수법에 의한 축대칭 원통형 셸의 자유진동 해석)

  • Choi, Myung-Soo;Yeo, Dong-Jun
    • Journal of Power System Engineering
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    • v.17 no.2
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    • pp.46-55
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    • 2013
  • In this paper, the computational algorithm for free vibration analysis of an axisymmetric cylindrical shell is formulated by the Sylvester-transfer stiffness coefficient method (S-TSCM) which combines the Sylvester's inertia theorem and the transfer stiffness coefficient method. After the computational programs for obtaining the natural frequencies and natural modes of the axisymmetric cylindrical shell are made by the S-TSCM and the finite element method (FEM), the computational results which are natural frequencies, natural modes, and computational times by both methods are compared. From the computational results, we can confirm that S-TSCM has the reliability in the free vibration analysis of the axisymmetric cylindrical shell and is superior to FEM in the viewpoint of computational times.

ADAPTIVE STABILIZATION OF NON NECESSARILY INVERSELY STABLE CONTINUOUS-TIME SYSTEMS BY USING ESTIMATION MODIFICATION WITHOUT USING HYSTERESIS FUNCTION

  • Sen, M.De La
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.29-53
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    • 2001
  • This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

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An Efficient Computational Method for Linear Time-invariant Systems via Legendre Wavelet (르장드르 웨이블릿을 이용한 선형 시불변 시스템의 효율적 수치 해석 방법)

  • Kim, Beomsoo
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.7
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    • pp.577-582
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    • 2013
  • In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet's integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

Eigenstructure Assignment for Linear Time-Varying Systems: a Differential Sylvester Equation Approach (미분 Sylvester 방정식을 이용한 선형 시변 시스템의 고유구조 지정기법)

  • 최재원;이호철
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.7
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    • pp.777-786
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    • 1999
  • This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

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Key Agreement Protocol Using Sylvester Hadamard Matrices

  • Choe, Chang-Hui;Lee, Moon-Ho
    • Journal of Communications and Networks
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    • v.13 no.3
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    • pp.211-213
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    • 2011
  • In this paper, we propose a key agreement protocol using Sylvester Hadamard matrices. Users obtain their common key by using a matrix shared in advance. Matrix construction is very simple, and the computation is quite fast. The proposal will be useful for communication between two users, especially for those having low computing power.

Controllability and Observability of Sylvester Matrix Dynamical Systems on Time Scales

  • Appa Rao, Bhogapurapu Venkata;Prasad, Krosuri Anjaneya Siva Naga Vara
    • Kyungpook Mathematical Journal
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    • v.56 no.2
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    • pp.529-539
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    • 2016
  • In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.

J. J. Sylvester, F. Klein and American Mathematics in 19th Century (실베스터와 클라인 그리고 19세기 미국 수학)

  • Lee Sang-Gu;Ham Yoon-Mee
    • Journal for History of Mathematics
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    • v.19 no.2
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    • pp.77-88
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    • 2006
  • In 1876, America's first Jewish math professor J. J. Sylvester took a department head position at the first research university in USA at the age of 61. He launched the America's first research journal of mathematics in 1877. We study the role and meaning of J. J. Sylvester, F. Klein and E. H. Moore in late 19th century of American mathematics from Korean's perspective.

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