• 대한수학회지
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• 제41권6호
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• pp.957-976
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• 2004

It is well known that the application of the nonlinear coordinate transformations is useful for efficient numerical evaluation of weakly singular integrals. In this paper, we consider the trapezoidal rule combined with a nonlinear transformation $\Omega$$_{m}$(b;$\chi$), containing a parameter b, proposed first by Yun [14]. It is shown that the trapezoidal rule with the transformation $\Omega$$_{m}$(b;$\chi$), like the case of the Gauss-Legendre quadrature rule, can improve the asymptotic truncation error by using a moderately large b. By several examples, we compare the numerical results of the present method with those of some existing methods. This shows the superiority of the transformation $\Omega$$_{m}$(b;$\chi$).TEX>).

• 설비공학논문집
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• 제16권8호
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• pp.691-697
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• 2004

Experimental study is carried out to investigate the heat transport capability and thermal resistance of sinusoidal axially grooved heat pipe, comparing its performance to trapezoidal axially grooved heat pipe. As a result from this work, the heat transport capability of sinusoidal grooved heat pipe is lower than that of trapezoidal grooved heat pipe for the same size of outer diameter. As the ratio of depth to width of sinusoidal groove heat pipe is higher, the heat transport capability of heat pipe becomes higher. It is found that Aluminum-ammonia heat pipes with sinusoidal and trapezoidal grooves have good thermal resistance, below 0.1$^{\circ}C$/W at evaporator section and below 0.05$^{\circ}C$/W at condenser section.

• 대한전자공학회논문지TC
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• 제46권2호
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• pp.134-140
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• 2009

본 논문에서는 마이크로스트립구조에서 $3.1{\times}10.6GHz$대역의 UWB 통신을 위한 사다리꼴 안테나모델에 대해 광대역화를 검토하였다. 두 사다리꼴의 마이크로스트립패치 치수를 서로 다르게 한 모노폴의 사다리꼴안테나 모델에 대해 컴퓨터 시뮬레이션을 통하여 UWB의 대역폭에서 반사손실 -10dB(VSWR<2)이하의 임피던스 정합특성을 보이는 안테나의 동작특성을 나타내 보였다. 또한, 본 논문에서 구한 최적화 안테나는 UWB의 전 대역에서 선형위상과 수평면내에서 대체로 무지향 방사특성을 나타내 보인다.

• Structural Engineering and Mechanics
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• 제3권2호
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• pp.145-162
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• 1995

A damped trapezoidal rule method for numerical time-integration is presented, and its application in analyses of dynamic response of damped structures is discussed. It is shown that the damped trapezoidal rule method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are developed for the damped single-degree-of-freedom systems. Error analyses are also performed for the Newmark beta method and compared with the damped trapezoidal rule method as a basis for discussion of the relative merits of the proposed method. The procedure is fully explicit and easy to implement. However, since the method is an explicit method, it is conditionally stable. The methodology is applied to several example problems to illustrate its strengths, limitations and inherent simplicity.

• Steel and Composite Structures
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• 제36권1호
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• pp.47-62
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• 2020

In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.593-605
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• 2002

Explicit hounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1996년도 춘계공동학술대회논문집; 공군사관학교, 청주; 26-27 Apr. 1996
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• pp.76-78
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• 1996

When data is classified and each class has weight, the mean of data is a weighted average. When the class values and weights are trapezoidal fuzzy numbers, we can prove the weghted average is a fuzzy number though not trapezoidal. Its 4 corner points are obtained.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2009년도 정기 학술발표대회
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• pp.117.1-117.1
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• 2009

• 한국전산유체공학회지
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• 제11권3호
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• pp.46-51
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• 2006

This paper presents the numerical results of fluid flow and mixing in a microfluidic device for electro-osmotic flow (EOF) with an trapezoidal electrode array on the bottom wall (ETZEA). Differently from previous EOF in a channel which only transports fluid in colloidal system. ETZEA can also be utilized to mix a target liquid with a reagent. In this study we propose a method of controlling fluid flow and mixing enhancement. To obtain the flow and mixing characteristics, numerical computations are performed by using a commercial code, CFX-10, and a self-made code LBM-D. It was found that the flow near the trapezoidal electrode in the ETZEA is of 3-D complex flows due to the zeta potential difference between the trapezoidal electrode and channel walls, and as a consequence the hetrogeneous zeta potential on the electrodes plays an important role in mixing the liquid.

• 한국전자파학회논문지
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• 제20권3호
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• pp.215-221
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• 2009

본 논문에서는 차량 GPS 안테나로 사용할 수 있는 프랙털 구조의 사다리꼴 마이크로스트립 패치 안테나를 설계하고 이를 제작하였다. 기판 손실을 없애고 이득을 향상시키기 위하여 공기층을 갖는 패치 안테나로 설계하였다. 사다리꼴 패치에 프랙털 구조의 적용과 슬롯의 부설로 일반 삼각형 패치 안테나 면적 대비 42.5 %크기로 소형화시켰다. 제작 후 측정한 결과, VSWR 2:1 기준으로 GPS 대역을 포함한 200 MHz의 대역폭을 얻었다. 이득은 공진주파수에서 4.31 dBi로 일반 세라믹 패치 안테나의 이득보다 GPS 대역에서 2$\sim$5 dB 높은 이득을 얻었다.