• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.923-930
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• 2010

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping, and in the second stage, damping matrices are estimated with the mass and stiffness matrices fixed. Three methods to estimate damping matrices for this purpose are proposed in this paper. The methods include one for proportional damping systems and two for non-proportional damping systems. Method 1 utilizes orthogonality of normal modes and estimates damping matrices using the modal parameters extracted from the measured responses. Method 2 estimates damping matrices from impedance matrices which are the inverse of FRF matrices. Method 3 estimates damping using the equation which relates a damping matrix to the difference between the analytical and measured FRFs. The characteristics of the three methods are investigated by applying them to simulated discrete system data and experimental cantilever beam data.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.19-29
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• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.245-256
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• 1994

A new axisymmetric crack model is proposed on the basis of p-version of the finite element method limited to theory of small scale yielding. To this end, axisymmetric stress element is formulated by integrals of Legendre polynomial which has hierarchical nature and orthogonality relationship. The virtual crack extension method has been adopted to calculate the stress intensity factors for 3-D axisymmetric cracked bodies where the potential energy change as a function of position along the crack front is calculated. The sensitivity with respect to the aspect ratio and Poisson locking has been tested to ascertain the robustness of p-version axisymmetric element. Also, the limit value that is an exact solution obtained by FEM when degree of freedom is infinite can be estimated using the extrapolation equation based on error prediction in energy norm. Numerical examples of thick-walled cylinder, axisymmetric crack in a round bar and internal part-thorough cracked pipes are tested with high precision.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.199-209
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• 2001

Modal analysis method (MAM) is introduced for the fully coupled structural dynamic problems. In this paper, the beam with active constrained layered damping (ACLD) treatment is considered as a representative problem. The ACLD beam consists of a viscoelastic layer that is sandwiched between the base beam structure and an active piezoelectric layer. The exact damped natural modes are spectrally formulated from a set of fully coupled dynamic equations of motion. The orthogonality property of the exact damped natural modes is then derived in a closed form to complete the modal analysis method. The accuracy of the present MAM is evaluated through some illustrative examples: the dynamic characteristics obtained by the present MAM are compared with the results by spectral element method (SEM) and finite element method (FEM). It is numerically proved that MAM solutions become identical to the accurate SEM solutions as the number of exact natural used in MAM is increased.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.445-450
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• 1997

Optimal design of a piezoelectric smart structure is studied for cabin noise control. A cubic shaped acoustic cavity with a flat plate which covers one side is taken as the problem. The sensor signal is returned to the actuator through a negative gain. The acoustic cavity is modeled using the modal approach which represents the pressure fields in the cavity as a sum of mode shapes of the cavity with unknown coefficients. By using orthogonality of the mode shapes of the cavity, finite element equation for the structure with the influence of the acoustic cavity is derived. The objective function is the average pressure at a certain region, so-called silent zone, in the cavity and the design variables are the locations and sizes of the piezoelectric actuator and sensor. The optimal design is performed at several frequencies and the results show a remarkable noise reduction.

• Journal of computational fluids engineering
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• v.6 no.1
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• pp.1-13
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• 2001

The natural convection heat transfer and solidification in a stratified pool are studied. The flow and heat transfer characteristics in a heat generating pool are compared between single-layered and double-layered pools. And local Nusselt number distributions on outer walls are obtained to consider thermal loads on a vessel wall. The cooling and solidification of Al₂O₃/Fe melt in a hemispherical vessel are simulated to study the mechanism of heat transfer and temperature distribution. A unstructured mesh is chosen for this study because of the non-orthogonality originated from the boundaries of double-layered pool. Interface between the layers is modeled to be fixed. With this assumption mass flux across the interface is neglected, but shear force and heat flux are considered by boundary conditions. The colocated cell-centered finite volume method is used with the Rhie-Chow interpolation to compute cell face velocity. To prevent non-physical solutions near walls in case body force is large the wall pressure is extrapolated by the way to include body force. The numerical solutions calculated by current method show that averaged downward heat flux of the double-layered pool increases compared to single-layered pool and maximum temperature occurs right below the interface of the layers.

• Structural Engineering and Mechanics
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• v.35 no.1
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• pp.53-65
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• 2010

The rigid body inertia properties of a structure including the mass, the center of gravity location, the mass moments and principal axes of inertia are required for structural dynamic analysis, modeling of mechanical systems, design of mechanisms and optimization. The analytical approaches such as solid or finite element modeling can not be used efficiently for estimating the rigid body inertia properties of complex structures. Several experimental approaches have been developed to determine the rigid body inertia properties of a structure via Frequency Response Functions (FRFs). In the present work two experimental methods are used to estimate the rigid body inertia properties of a frame. The first approach consists of using the amount of mass as input to estimate the other inertia properties of frame. In the second approach, the property of orthogonality of modes is used to derive the inertia properties of a frame. The accuracy of the estimated parameters is evaluated through the comparison of the experimental results with those of the theoretical Solid Work model of frame. Moreover, a thorough discussion about the effect of accuracy of measured FRFs on the estimation of inertia properties is presented.

• Journal of KSNVE
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• v.8 no.3
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• pp.428-434
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• 1998

Optimal design of a piezoelectric smart structure is studied for cabin noise control. A cubic shaped acoustic cavity with a flat plate which covers one side is taken as the problem. The sensor signal is returned to the actuator through a negative gain. The acoustic cavity is modeled using the modal approach which represents the pressure fields in the cavity as a sum of mode shapes of the cavity with unknown coefficients. By using orthogonality of the mode shapes of the cavity, finite element equation for the structure with the influence of the acoustic cavity is derived. The objective function is the average pressure at a certain region, so-called silent zone, in the cavity and the design variables are the locations and sizes of the piezoelectirc actuator and sensor. The optimal design is performed at several frequencies and the results show a remarkable noise reduction. To see the robustness of the optimally designed result, the configuration is used to examine the noise reduction at different frequencies. By adjusting the gain at each frequencies, it is possible to reduce the noise in comparison with the result when the actuator is not activated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.3
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• pp.173-182
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• 2013

The building design projects which are being proceeded nowadays pursue a complex and various shape of structures, escaping from the traditional and regular shape of buildings. In this new trend of the architecture, there rises a demand of the research in the structural engineering for the effective realization of such complex-shaped buildings which disassembles the orthogonality of frames. As a distinguished characteristics of the buildings in a complex-shape, there frequently are inclined columns included in the structural frame. The inclined column causes extra axial force and bending moment at the beam-column connection so it is necessary to assess those effects on the structural behavior of the frame and the connection by experiment or analysis. However, with comparing to the studies on the normal beam-column connections, the inclined column connections have not been studied sufficiently. Therefore, this study evaluated the beam-column connections having an inclined column using nonlinear and finite element analysis method. In this paper, steel moment frames having inclined columns were analyzed by the nonlinear pushover analysis to check the global behavior and beam-column connection models were analyzed by the finite element analysis to check the buckling behavior and the fracture potentials.