• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.551-566
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• 2005

Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotatory inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.647-664
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• 2006

In this study, an improved finite element formulation with a scheme of solution for the large deflection analysis of inextensible prismatic and nonprismatic slender beams is developed. For this purpose, a three-noded Lagrangian beam-element with two dependent degrees of freedom per node (i.e., the vertical displacement, y, and the actual slope, $dy/ds=sin{\theta}$, where s is the curved coordinate along the deflected beam) is used to derive the element stiffness matrix. The element stiffness matrix in the global xy-coordinate system is achieved by means of coordinate transformation of a highly nonlinear ($6{\times}6$) element matrix in the local sy-coordinate. Because of bending with large curvature, highly nonlinear expressions are developed within the global stiffness matrix. To achieve the solution after specifying the proper loading and boundary conditions, an iterative quasi-linearization technique with successive corrections are employed considering these nonlinear expressions to remain constant during all iterations of the solution. In order to verify the validity and the accuracy of this study, the vertical and the horizontal displacements of prismatic and nonprismatic beams subjected to various cases of loading and boundary conditions are evaluated and compared with analytic solutions and numerical results by available references and the results by ADINA, and excellent agreements were achieved. The main advantage of the present technique is that the solution is directly obtained, i.e., non-incremental approach, using few iterations (3 to 6 iterations) and without the need to split the stiffness matrix into elastic and geometric matrices.

• Architectural research
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• v.10 no.1
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• pp.25-32
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method to study parametrical instability of lattice dome structures, which is subjected to harmonically pulsating load. We consider elastic stiffness and geometrical stiffness simultaneously during the calculation of stiffness matrix, and adopt consistent mass matrix to make the solution more correct. In order to obtain instability regions, we represent displacements and accelerations in dynamic equation by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability regions eventually. Finally, we take 24-bar star dome and 90-bar lamella dome as examples to investigate dynamic instability phenomena.

• Journal of Korean Association for Spatial Structures
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• v.2 no.2 s.4
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• pp.59-67
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• 2002

In this study, a method that estimates stiffness and mass matrices of shear building from modal test data is presented. This method applied of building depends on the number of measurement points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured. By means of this method it is possible to use modal data of unmeasurable points to estimate total stiffness and mass matrices of structure. Some examples are studied in this paper, and its result shows that this method is reliable.

• Journal of Power System Engineering
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• v.3 no.1
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• pp.74-79
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• 1999

This paper describes formulation for algorithm of time historical response analysis of vibration for straight-line structure. This method is derived from a combination of the transfer stiffness coefficient method and the Newmark method. And this present method improves the computational accuracy of the transient vibration response analysis remarkably owing to several advantages of the transfer stiffness coefficient method. We regarded the structure as a lumped mass system here. The analysis algorithm for the time historical response was formulated for the straight-line structure containing crooked, tree type system. The validity of the present method compared with the transfer matrix method and the Finite Element Method for transient vibration analysis is demonstrated through the numerical computations.

• Proceedings of the KSR Conference
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• 2004.10a
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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.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.786-791
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• 2004

This study proposed the analysis of mass position detection and modified stiffness due to the change of the mass and stiffness of structure by using the original and modified dynamic characteristics. The method is applied to examples of a cantilever and 3 degree of freedom by modifying the mass. The predicted detection of mass positions and magnitudes are in good agreement with these from the structural reanalysis using the modified mass.

• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.1
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• pp.77-84
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• 2011

This study is to develop nonlinear analysis algorithm for transfer matrix method, which can be applied to continuous beam analysis. Gauss-Lobatto integral rule is adopted and the transfer matrix is derived from stiffness matrix. In the transfer matrix method, the system equation has a constant number of unknowns regardless of number of D.O.F. Therefore, the transfer matrix method has computational efficiencies not only in linear elastic analysis but also in nonlinear analysis. To verify the developed method, the analysis results of several examples are compared with commercial code in moment-curvature, moment-displacement and load-displacement relation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.351-363
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• 2004

Equation of motion of non conservative system considering mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory force's direction change and Winkler and Pasternak foundation stiffness matrix is derived. Also stability analysis due to the divergence and flutter loads is performed. And the influence of internal and external damping coefficient on flutter load is investigated applying the quadratic eigen problem solution. Additionally the influence of non-conservative force's direction parameter, internal and external damping and Winkler and Pasternak foundation on the critical load of Beck's and Leipholz's and Hauger's columns are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.971-980
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• 1997

This study is to investigate the stiffness degradation of a composite laminated panel including transverse matrix cracks subjected to bending and twisting moments. Micromechanics theory on the composite material is derived by introducing crack density. Iterative numerical scheme is developed to calculate the degraded composite stiffness which has nonlinear relation due to the crack density. The finite element method is used for structural analysis of the composite panel. Structural responses of the composite panel are examined for various laminated angles and crack density under the bending and twisting moments. Also, the effect of crack opening and closing is considered in the examination. It is realized that the matrix cracks may cause severe stiffness reduction and should be considered in the composite laminated panel.