• 한국산학기술학회논문지
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• 제16권4호
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• pp.2370-2378
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• 2015

본 논문에서는 로봇 매니퓰레이터의 토크 최소화를 위한 궤적계획을 위해 라그랑지 보간법을 이용한 Algorithm을 제안하였다. 이를 위해 로봇 매니퓰레이터의 위치에 대한 구속조건이 주어지고 안정성이 보장되어야 한다. 라그랑지 보간법의 Runge's 현상을 회피하기 위해 Chebyshev 보간점을 이용하여 시간 보간점을 설정하였고, 이에 대응하는 최적각도를 찾아내어 라그랑지 보간법을 이용한 매끄러운 관절의 각도, 속도, 가속도 궤적을 얻을 수 있다. 로봇 매니퓰레이터의 토크 소비 최적화를 위한 성능지표를 선정하였으며, 계산된 궤적을 통해 이 성능지표가 최소값을 가지도록 반복 계산하는 과정을 거친다. 이를 통해, 토크와 성능지표를 최소화 시키는 최적의 궤적을 얻을 수 있으며, 로봇 매니퓰레이터가 작업을 수행하기 위한 움직임의 안전성을 보장한다.

• Coupled systems mechanics
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• 제1권2호
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• 제83권1호
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• pp.67-77
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• 2022

In this study, frictionless continuous and discontinuous contact problems of a magneto-electro-elastic layer in the presence of the body force were discussed. The layer was indented by a rigid cylindrical insulating punch and supported by a rigid substrate without bond. Applying the Fourier integral transform technique, the general expressions of the problem were derived in the presence of body force. Thanks to the boundary conditions, the singular integral equations were obtained for both the continuous and the discontinuous contact cases. Gauss-Chebyshev integration formulas were used to transform the singular integral equations into a set of nonlinear equations. Contact width under the punch, initial separation distance, critical load, separation regions and contact stress under the punch and between the layer, and substrate were given as a result.

• International Journal of Naval Architecture and Ocean Engineering
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• 제4권1호
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• pp.9-19
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• 2012

A set of equations of motion is derived for vibratory motions of an underwater cable connected to a moving vehicle at one end and with drogues at the other end. From the static analysis, cable configurations are obtained for different vehicle speeds and towing pretensions are determined by fluid resistance of drogues. Also the dynamic analysis is required to predict its vibratory motion. Nonlinear fluid drag forces greatly influence the dynamic tension. In this study, a numerical analysis program was developed to find out the characteristic of cable behaviour. The motion is described in terms of space and time coordinates based on Chebyshev polynomial expansions. For the spatial integration the collocation method is employed and the Newmark method is applied for the time integration. Dynamic tensions, displacements, velocities, accelerations were predicted in the time domain while natural frequencies and transfer functions were obtained in the frequency domain.

• 전산구조공학
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• 제6권2호
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• pp.95-102
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• 1993

노후 구조물의 안전진단을 위하여 동적재하시험을 수행하고 그 결과를 유한요소모델과 같은 해석적 모델과 결합하여 기존구조물의 강성평가 및 파손부위 색출에 적용하고 있는데 측정점의 제한성과 유한요소모델의 많은 자유도가 측정데이타를 유한요소모델과 연계하는데 커다란 문제점으로 대두된다. 본 연구에서는 유한요소모델과 같이 많은 자유도를 갖는 구조계의 해석적 모델을 측정데이타와 결합하기 위하여 축약된 좌표계에서 구조계의 동강성행렬(dynamic stiffness matrix)표현방법을 제시하였다. 유한요소모델로부터 좌표계를 축약시 필연적으로 발생되는 주파수의존성(frequency dependency)을 고려하기 위하여 주파수영역에서 Chebyshev다항식으로 축약된 동강성행렬을 표시하였고 특이점에서 발생되는 악조건(ill-condition)을 극복하기 위하여 특이해분리(singular value decomposition)기법을 사용하였다. 제시된 방법의 검증을 위하여 간단한 구조계에 대하여 시뮬레이션을 수행하였으며 본 방법으로 수립된 구조계의 동적모델은 축약이전의 전체계에 대한 동적특성을 비교적 정확히 유지하고 있고 일반적으로 사용되는 정적축약 형태의 수학적 모델보다 우수함을 알 수 있었다.

• 한국수산과학회지
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• 제44권4호
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• pp.413-422
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• 2011

An improved split-beam transducer for a 50 kHz fish-sizing echo sounder was developed. The main objective of this study was to minimize the side lobe level in the beam pattern and the distance between acoustic centers for adjacent transducer quadrants in the geometrical arrangement of array elements while maintaining a given number of transducer elements and beam width. To achieve these goals, a 32-element planar array transducer ($6{\times}6$ array with one element in each corner missing) was designed using the Dolph-Chebyshev shading function to suppress side lobes in the array beam pattern and fabricated by arranging the inter-element spacing to be substantially equal to half the wavelength using the transducer element of 0.4 times the wavelength in diameter. The performance characteristics of this split-beam transducer were evaluated in the experimental water tank of $5m{\times}5m{\times}6m$ (length${\times}$height${\times}$width). In this study, the design goal of the beam width and side lobe level for transmitting a beam pattern was initially set at $21^{\circ}$ and -30 dB, respectively. However, the measured beam width at 3 dB was $21^{\circ}$ in both directions with side lobe levels of -24.7 dB in the horizontal plane and -25.6 dB in the vertical plane. The averaged beam width at -3 dB of the receiving beam patterns for four receiving quadrants was $31.4^{\circ}$. The transmitting voltage response was 161.5 dB (re $1{\mu}Pa$/V at 1 m) at 50.23 kHz with a bandwidth of 2.16 kHz, and the averaged receiving sensitivity for four receiving quadrants was -178.13 dB (re 1 V/${\mu}Pa$) at 49.8 kHz with a bandwidth of 2.64 kHz.