• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1071-1074
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• 2006

The frequency response functions and loss factors, $\eta$, of structurally hollowed, rectangular, metal cantilever beams have been measured in bending vibrations within low strain amplitudes. The beams were heat treated or fined with aluminum to vary the material conditions. The measured frequency response functions at the end of the cantilevered beam were processed to calculate the structural damping ratios. The results showed that the modal frequencies and damping ratios of heat treated beam are increased due to the increase of beam rigidity with the predictions of the classical beam theory. When the beams are fined with aluminum, however, the frequencies are decreased due to the increase of mass, while the damping ratios are increased. As the agreement between measurement and classical theory is good, the performance of a beam with heat treated or fined with dissimilar material can be duplicated, for industrial and most practical purposes, by the theory developed for an internally damped homogeneous beam.

• Steel and Composite Structures
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• v.39 no.5
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.24 no.7
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• pp.578-583
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• 2011

We report on the design of a holographic homogenizer composed of a periodic hologram and a condensing lens. If the hologram is periodic, the homogenizer is free from the alignment error of the incident laser beam. Holographic homogenizer also has an advantage of the flexibility in the size of the target beam. We calculated theoretically the Fraunhofer diffracted wave function when a rectangular laser beam is incident on a periodic hologram. The diffracted wave is the sum of sinc functions at regular distance. The width of each sinc function depends on the size of the incident laser beam and the distance between the sinc functions depends on the period of the hologram. We calculated numerically the diffracted light intensity for various ratios of the size of the incident laser beam to the period of the hologram. The results show that it is possible to make the diffracted beam uniform at a certain value of the ratio. The uniformity is high at the central part of the target area and low near the edge. The more sinc functions are included in the target area, the larger portion of the area becomes uniform and the higher is the uniformity at the central part. Therefore, we can make efficient homogenizer if we design a hologram so that the maximum number of the diffracted beams may be included in the target area.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.455-470
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• 2016

In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.143-148
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• 2000

In this article, we presents multi-objective design optimization of laminated composite beam using Fuzzy programming method. At first, the two design objectives are minimizing the structural weight and maximizing the buckling load respectively. Fuzzy multi-optimization problem can be formulated based on results of single optimizations. Due to different relative importance of design objectives, membership functions are constructed by adding exponential parameters for different objective's weights. Finite element analysis of composite beam for buckling behavior are carried by Natural mode method proposed by J.Argyris and computational time of analysis can be reduced. With this scheme, a designer can conveniently obtain a compromise optimal solution of a multi-objective optimization problem only by providing some exponential parameters corresponding to the importance of the objective functions.

• The Journal of the Acoustical Society of Korea
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• v.21 no.2E
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• pp.63-70
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• 2002

In this paper, an optimization technique for thin walled beams of vehicle body structure is proposed. Stiffness of thin walled beam structure is characterized by the thickness and typical section shape of the beam structure. Approximate functions for the section properties such as area, area moment of inertia, and torsional constant are derived by using the response surface method. The approximate functions can be used for the optimal design of the vehicle body that consists of complicated thin walled beams. A passenger car body structure is optimized to demonstrate the proposed technique.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.623-628
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• 2004

In this study, the assumed-mode method using characteristic polynomials of Timoshenko beam is applied for the free vibration analysis of rectangular stiffened plates. The polynomial is derived considering the rotational constraint along the boundary edges of plate and the orthogonal relation of Timoshenko beam functions, which enables to simplify the free vibration analysis of plate structure having various boundary conditions. To verify the validity and effectiveness of the adopted method, numerical analysis for cross-stiffened plates were carried out and its results were compared with those obtained by the general purpose FEA software.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.570-579
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• 2011

This paper deals with free vibrations of the circular curved beams with constant volume, whose cross sectional shapes are the circular solid cross-sections. Volumes of the objective beam are always held in constant regardless shape functions of the cross-sectional radius. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such beam are derived and solved numerically for determining the natural frequencies. In numerical examples, the hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, relationships between frequency parameters and various beam parameters such as rise ratio, section ratio, elasticity ratio, volume ratio, slenderness ratio and taper type are reported in tables and figures.

• Structural Engineering and Mechanics
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• v.7 no.4
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• pp.361-375
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• 1999

This paper presents an analytic method of examining the out-of-plane vibration of continuous curved beam on periodical supports. The orthogonality of two distinct sets of mode shape functions is derived. The forced vibration of beam due to moving loads is examined. Two types of moving loads, which are concentrated load and uniformly distributed load, are considered. The response characteristics of beam induced by these loads are investigated as well.