• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.179-186
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• 2016

This paper presents a numerical method that can evaluate the effect of crack for the in-plane bending vibration of Timoshenko beam. The method is a transfer matrix method that the element transfer matrix is deduced from the element dynamic stiffness matrix. An edge crack is expressed as a rotational spring, and then is formulated as an independent transfer matrix. To demonstrate the accuracy of this theory, the results computed from the present are compared with those obtained from the commercial finite element analysis program. Based on these comparison results, a parametric study is performed to analyze the effects for the size and locations of crack.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.73-80
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• 2004

Mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory non-conservative force, and Winkler and Pasternak foundation matrix of framed structure in 2-D are calculated for stability analysis of divergence or flutter system. Then, a matrix equation of the motion for the non-conservative system is formulated and numerical results are presented to demonstrate the effect of some parameters with using Newmark method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.4 s.247
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• pp.387-392
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• 2006

This paper predicts the modified mass and stiffness of structure using the sensitivity coefficients with the iterative method. The sensitivity coefficients are obtained by the change of the eigenvectors according to structural modification. The method is applied to an examples of a 3 degree of freedom system by modifying mass and stiffness. The predicted mass and stiffness are in good agreement with these from the structural reanalysis using the modified mass and stiffness.

• International Journal of Precision Engineering and Manufacturing
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• v.4 no.1
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• pp.15-22
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• 2003

Beams are often subject to bending-torsion coupled vibration due to mass coupling and/or stiffness coupling. This paper proposes a dynamic analysis method using the exact dynamic element for bending-torsion coupled vibration of general plane beam structures with joints. The exact dynamic element matrix for a bending-torsion coupled beam is derived, and the detailed procedure of using the exact dynamic element matrix is also presented. Three examples are provided for validating and illustrating the proposed method. The numerical study proves the proposed method to be useful for dynamic analysis of bending-torsion coupled beam structures with joints.

• Steel and Composite Structures
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• v.39 no.5
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• pp.543-564
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• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.10
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• pp.1056-1061
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• 2012

FEM analysis is essential to shorten the development time and reduce the cost for developing high-performance machine tools. Mount joint parts play important role to ensure static and dynamic stability of machine tools. This paper suggests a computational modeling of mount joint part of machine tools. MATRIX27 element of ANSYS is adopted to model mount joint parts. MATRIX27 allows the definition of stiffness and damping matrices in matrix form. The matrix is assumed to relate two nodes, each with six degrees of freedom per node. Stiffness and damping values of commercial mount products are measured to build a database for FEM analysis. Jack mounts with rubber pad are exemplified in this paper. The database extracted from the experiments is also used to estimate of stiffness and damping of untested mounts. FEM analysis of machine tools system with the suggested mount computational model is performed. Static and dynamic results prove the feasibility of the suggested mount model.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.355-360
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• 2001

By using Frenet formulation and Timoshenko beam theory, the partial differential equations of motion are derived for a helical spring having a doubly symmetrical cross section subjected to the pre-load axially. These equations of motion are solved to give the dispersion relationship and dynamic stiffness matrix is assembled. Natural frequencies are obtained from the receptance of the system. The results of the dynamic stiffness method are compared with those of the transfer matrix method from published examples and finite element method.

• Smart Structures and Systems
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• v.9 no.1
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• pp.55-70
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• 2012

It is not easy to experimentally obtain the FRF (Frequency Response Function) matrix corresponding to a full set of DOFs (degrees of freedom) for a dynamic system. Utilizing FRF data measured at specific positions, with DOFs less than that of the system, as constraints to describe a damaged system, this study identifies parameter matrices such as mass, stiffness and damping matrices of the system, and provides a damage identification method from their variations. The proposed parameter identification method is compared to Lee and Kim's method and Fritzen's method. The validity of the proposed damage identification method is illustrated in a simple dynamic system.

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.291-310
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• 2014

An advanced model for the linear flutter analysis is introduced in this paper. Higher-order beam structural models are developed by using the Carrera Unified Formulation, which allows for the straightforward implementation of arbitrarily rich displacement fields without the need of a-priori kinematic assumptions. The strong form of the principle of virtual displacements is used to obtain the equations of motion and the natural boundary conditions for beams in free vibration. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out free vibration analyses. According to the doublet lattice method, the natural mode shapes are subsequently used as generalized motions for the generation of the unsteady aerodynamic generalized forces. Finally, the g-method is used to conduct flutter analyses of both isotropic and laminated composite lifting surfaces. The obtained results perfectly match those from 1D and 2D finite elements and those from experimental analyses. It can be stated that refined beam models are compulsory to deal with the flutter analysis of wing models whereas classical and lower-order models (up to the second-order) are not able to detect those flutter conditions that are characterized by bending-torsion couplings.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.2
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• pp.109-116
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• 2010

It is important to make a mechanical structure precisely and reasonably in predicting the dynamic characteristics, controlling the vibration, and designing the structure dynamics. In finite element analysis model updating is appropriate as the design parameter is used to analyze the dynamic system. The errors can be contained from the physical parameters and the element modeling. From the dynamic test, more precise dynamic characteristics can be obtained. In this paper, model updating algorithm is developed using frequency difference between experiment and calculation. Modal frequencies are obtained by experiment and finite element analysis for beams with various cross section and shapes which have added masses and holes in the middle. For plates with and without groove, experiment and analyses are carried out by applying free boundary conditions as well. Mass and stiffness matrices are updated by comparing test and analytical modal frequencies. The result shows that the updated frequencies become closer to the test frequencies in case that both matrices are updated. An improved analytical model is obtained by changing model parameters such that the discrepancy between test and finite element frequencies is minimized. For beam and plate models updating of mass and stiffness matrices can improve the dynamical behavior of the model by acting on the physical parameters such as masses and stiffness.