• Geomechanics and Engineering
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• 제1권2호
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Structural Engineering and Mechanics
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• 제7권1호
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• pp.81-94
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• 1999

The dynamic analysis of trusses using the finite element method tends to overlook the effect of local member dynamic behavior on the overall response of the complete structure. This is due to the fact that the lateral inertias of the members are omitted from the global inertia terms in the structure mass matrix. In this paper a condensed dynamic stiffness matrix is formulated and used to calculate the exact dynamic properties of trusses without the need to increase the model size. In the examples the limitations of current solutions are presented together with the exact results obtained from the proposed method.

• 대한기계학회논문집A
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• 제27권10호
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• pp.1653-1660
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• 2003

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 춘계학술대회 논문집
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• pp.536-543
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• 2005

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.759-769
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• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.399-408
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• 2018

Cable supported structures have been widely used in civil engineering. Cable tension estimation has great importance in cable supported structures' analysis, ranging from design to construction and from inspection to maintenance. Even though the Bernoulli-Euler beam element is commonly used in the traditional finite element method for calculation of frequency and cable tension estimation, many elements must be meshed to achieve accurate results, leading to expensive computation. To improve the accuracy and efficiency, a dynamic finite element method for estimation of cable tension is proposed. In this method, following the dynamic stiffness matrix method, frequency-dependent shape functions are adopted to derive the stiffness and mass matrices of an exact beam element that can be used for natural frequency calculation and cable tension estimation. An iterative algorithm is used for the exact beam element to determine both the exact natural frequencies and the cable tension. Illustrative examples show that, compared with the cable tension estimation method using the conventional beam element, the proposed method has a distinct advantage regarding the accuracy and the computational time.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.906-915
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• 2004

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using clement force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• 한국강구조학회 논문집
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• 제13권6호
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• pp.703-713
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• 2001

비대칭단면을 갖는 박벽 직선보의 3차원 자유진동해석을 수행하기 위하여 엄밀한 요소강도행렬을 유도한다. 단면이 균일한 비대칭 박벽 탄성보에 대하여 운동방정식, 힘-변위 관계식을 유도하고 엄밀한 동적강도행렬을 수치적으로 산정하는 방법을 제시한다. 14개의 변위파라미터를 도입하여 고차의 연립미분방정식을 1차 연립미분방정식으로 바꾸고, 비대칭행렬을 갖는 선형 고유치문제의 해를 복소수영역에서 구한다. 이를 이용하여 절점변위에 대한 처짐함수을 엄밀히 구하고, 재단력-변위 관계식을 이용하여 엄밀한 동적요소강도행렬을 산정한다. 본 방법의 타당성을 보이기 위하여 비대칭 박벽보의 고유진동수를 계산하고, 해석해, 혹은 3차 Hermitian 다항식을 사용한 보요소 및 ABAQUS를 사용한 유한요소 해석결과와 비교한다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.43-50
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• 2002

Main goal of this study is to develop MATLAB programming for exact analysis of distortional deformation of the straight box girder. For this purpose, a theory for distortional deformation theory is firstly summarized and then a BEF (Beam on Elastic Foundation) theory is presented using analogy of the corresponding variables. Finally, the governing equation of the beam-column element on elastic foundation is derived. An element stiffness matrix of the beam element is established via a generalized linear eigenvalue problem. In order to verify the efficiency and accuracy of the element using exact dynamic stiffness matrix, buckling loads for the continuous beam structures with elastic foundation and distortional deformations of box girders are calculated.

• 소음진동
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• 제9권1호
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• pp.103-112
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• 1999

A new modeling and analysis technique for one-dimensional distributed parameter systems is presented. First. discretized equations of motion in Laplace domain are derived by applying discretization methods for partial differential equations of a one-dimensional structure with respect to spatial coordinate. Secondly. the z and inverse z transformations are applied to the discretized equations of motion for obtaining a dynamic matrix for a uniform element. Four different discretization methods are tested with an example. Finally, taking infinite on the number of step for a uniform element leads to an exact dynamic matrix for the uniform element. A generalized modal analysis procedure for eigenvalue analysis and modal expansion is also presented. The resulting element dynamic matrix is tested with a numerical example. Another application example is provided to demonstrate the applicability of the proposed method.