• 제목/요약/키워드: Closed Form Solution

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A general closed-form solution to a Timoshenko beam on elastic foundation under moving harmonic line load

  • Luo, Wei-Li;Xia, Yong;Zhou, Xiao-Qing
    • Structural Engineering and Mechanics
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    • 제66권3호
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    • pp.387-397
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    • 2018
  • In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy's residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.

Closed-form solution of axisymmetric deformation of prestressed Föppl-Hencky membrane under constrained deflecting

  • Lian, Yong-Sheng;Sun, Jun-Yi;Dong, Jiao;Zheng, Zhou-Lian;Yang, Zhi-Xin
    • Structural Engineering and Mechanics
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    • 제69권6호
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    • pp.693-698
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    • 2019
  • In this study, the problem of axisymmetric deformation of prestressed $F{\ddot{o}}ppl-Hencky$ membrane under constrained deflecting was analytically solved and its closed-form solution was presented. The small-rotation-angle assumption usually adopted in membrane problems was given up, and the initial stress in membrane was taken into account. Consequently, this closed-form solution has higher calculation accuracy and can be applied for a wider range in comparison with the existing approximate solution. The presented numerical examples demonstrate the validity of the closed-form solution, and show the errors of the contact radius, profile and radial stress of membrane in the existing approximate solution brought by the small-rotation-angle assumption. Moreover, the influence of the initial stress on the contact radius is also discussed based on the numerical examples.

Natural Frequencies of Beams with Step Change in Cross-Section

  • Kim, Yong-Cheul;Nam, Alexander-V.
    • 한국해양공학회지
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    • 제18권2호
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    • pp.46-51
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    • 2004
  • Natural frequencies of the transverse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

자기동조 가중최소자승법을 이용한 AOA 측위 알고리즘 개발 (Development of an AOA Location Method Using Self-tuning Weighted Least Square)

  • 이성호;김동혁;노기홍;박경순;성태경
    • 제어로봇시스템학회논문지
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    • 제13권7호
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    • pp.683-687
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    • 2007
  • In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

Development of an AOA Location Method Using Covariance Estimation

  • Lee, Sung-Ho;Roh, Gi-Hong;Sung, Tae-Kyung
    • 한국항해항만학회:학술대회논문집
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    • 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.1
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    • pp.485-489
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    • 2006
  • In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and closed-form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a self-tuning weighted least square AOA algorithm that is a modified version of the conventional closed-form solution. In order to estimate the error covariance matrix as a weight, two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

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A closed-form solution for a fluid-structure system: shear beam-compressible fluid

  • Keivani, Amirhossein;Shooshtari, Ahmad;Sani, Ahmad Aftabi
    • Coupled systems mechanics
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    • 제2권2호
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    • pp.127-146
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    • 2013
  • A closed-form solution for a fluid-structure system is presented in this article. The closed-form is used to evaluate the finite element method results through a numeric example with consideration of high frequencies of excitation. In the example, the structure is modeled as a cantilever beam with rectangular cross-section including only shear deformation and the reservoir is assumed semi-infinite rectangular filled with compressible fluid. It is observed that finite element results deviate from the closed-form in relatively higher frequencies which is the case for the near field earthquakes.

Load-carrying capacities and failure modes of scaffold-shoring systems, Part II: An analytical model and its closed-form solution

  • Huang, Y.L.;Kao, Y.G.;Rosowsky, D.V.
    • Structural Engineering and Mechanics
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    • 제10권1호
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    • pp.67-79
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    • 2000
  • Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

Time-dependent analysis of cable trusses -Part I. Closed-form computational model

  • Kmet, S.;Tomko, M.
    • Structural Engineering and Mechanics
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    • 제38권2호
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    • pp.157-169
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    • 2011
  • In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

A Closed-Form Solution of Linear Spectral Transformation for Robust Speech Recognition

  • Kim, Dong-Hyun;Yook, Dong-Suk
    • ETRI Journal
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    • 제31권4호
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    • pp.454-456
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    • 2009
  • The maximum likelihood linear spectral transformation (ML-LST) using a numerical iteration method has been previously proposed for robust speech recognition. The numerical iteration method is not appropriate for real-time applications due to its computational complexity. In order to reduce the computational cost, the objective function of the ML-LST is approximated and a closed-form solution is proposed in this paper. It is shown experimentally that the proposed closed-form solution for the ML-LST can provide rapid speaker and environment adaptation for robust speech recognition.

An Asymptotic Solution and the Green's Function for the Transverse Vibration of Beams with Variable Properties

  • 김용철
    • 한국해양공학회지
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    • 제24권1호
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    • pp.34-38
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    • 2010
  • An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.