• Journal of Welding and Joining
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• 제25권3호
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• pp.85-91
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• 2007

The conventional study on the laser surface transformation hardening has been carried out with a beam of the specified shape and uniform power-intensity distribution in order to ensure the uniformity of the hardening depth. Two types of beams - the circular gaussian beam and rectangular beam of the uniform power-intensity distribution were used in this study. we were supposed to optimize the process parameters and to compare the hardening results with two optics respectively. As a result, the hardness distribution of the hardened zone was similar in both cases and the hardened phase by the rectangular beam was denser than that by the circular gaussian beam.

• 한국자동차공학회논문집
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• 제13권5호
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• pp.1-6
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• 2005

In this paper, the natural frequencies of non-homogeneous damped beam are determined by using the differential transformation. The beam considered has different stiffness, damping and mass properties in each of two parts. The various boundary conditions are assumed at each end. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving a non-homogeneous damped beam problem.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.1060-1065
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• 2002

In this paper, the numerical analysis of beam rest ing on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.402.2-402
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• 2002

In this paper, the numerical analysis of beam resting on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.690-695
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• 2003

The main purpose of this paper is to apply differential transformation method to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. The governing equation of motion of beam with open cracks on elastic foundation is derived. The concept of differential transformation is briefly introduced. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.165-172
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• 2023

This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.

• Structural Monitoring and Maintenance
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• 제4권1호
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• pp.33-52
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• 2017

A cantilever beam with a breathing crack is studied to improve the breathing crack identification sensitivity by the parametric optimization of sample entropy and wavelet transformation. Crack breathing is a special bi-linear phenomenon experienced by fatigue cracks which are under dynamic loadings. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a fatigue crack. To improve the sensitivity of entropy measurement for crack identification, wavelet transformation is merged with entropy. The crack identification is studied under different sinusoidal excitation frequencies of the cantilever beam. It is found that, for the excitation frequencies close to the first modal frequency of the beam structure, the method is capable of detecting only 22% of the crack depth percentage ratio with respect to the thickness of the beam. Using parametric optimization of sample entropy and wavelet transformation, this crack identification sensitivity is improved up to 8%. The experimental studies are carried out, and experimental results successfully validate the numerical parametric optimization process.

• Journal of Advanced Marine Engineering and Technology
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• 제31권8호
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• pp.961-969
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• 2007

The laser material processing has replaced a conventional material processing such as a welding, cutting, drilling and surface modification and so on. LTH(Laser Transformation Hardening) is one branch of the laser surface modification process. A lot of energy is needed for the LTH process to elevate workpiece surface to temperature of the austenite transformation($A_3$), which results from utilizing a beam with a larger size and lower power intensity comparatively. The absorptivity of the laser energy with respect to material depends on the wave length of a beam. This study is related to the surface hardening for the rod-shaped carbon steel by the high power diode laser(HPDL) whose beam absorptivity is better than conventional types of lasers such as $CO_2$ or Nd:YAG laser. Because a beam proceeds on the rotating specimen the pretreated hardened-phase can be tempered and softened by the overlapping between hardened tracks. Accordingly, the longitudinal hardness measurement and observation of the micro structure was carried out for an assessment of the hardening characteristics. In addition, a hardening characteristics as a hardenability of materials was compared in the point of view of the hardness distribution and hardening depth and width.

• 한국광학회지
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• 제32권6호
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• pp.276-285
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• 2021

본 논문은 디스플레이용 OLED의 제작 공정에 사용하는 레이저 박리(laser lift-off, LLO) 장비의 선형빔 광학계에 대한 연구로서, M²가 큰 레이저를 사용하는 경우, 단축의 선폭을 작게 만들면서 공정심도를 깊게 유지하기 위한 빔 변환 모듈(beam transformation unit, BTU)을 포함한 광학계에 대한 연구를 진행하였고, 단축 형상을 슈퍼 가우시안으로 만들 수 있는 방법과 flat-top 분포로 만들 수 있는 광섬유를 사용하는 빔 변환 방식에 대하여 제시하였다.

• Structural Engineering and Mechanics
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• 제31권4호
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• pp.383-392
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• 2009

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.