쿨롱마찰을 갖는 단자유도계의 자유진동응답에 관한 닫힌 해

이성경 한국전산구조공학회 2020 한국전산구조공학회논문집 Vol.33 No.1

The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness. 본 연구는 쿨롱마찰을 갖는 동적시스템의 기초적인 연구로써 단자유도계의 자유진동응답에 대한 닫힌 해를 제공하는 것을 목적으로 한다. 쿨롱마찰을 포함하는 동적시스템의 운동방정식은 운동방향에 따른 마찰력의 부호변화로 인하여 비선형 미분방정식의 형태로 표현되기 때문에 닫힌 형태의 해를 얻기가 매우 어려운 특성이 있다. 이를 해결하기 위한 기존의 방법으로는 수치적분법에 의해 비선형 미분방정식을 직접 계산하거나 또는, 쿨롱마찰에 의한 감쇠효과를 등가점성감쇠로 치환한 선형 미분방정식을 이용하여 간접적으로 해를 구하는 방법이 사용되고 있다. 그러나 이러한 방법들은 수학적인 측면에서 닫힌 해를 제공하지 않는다. 따라서 본 연구에서는 운동방정식에서 반주기 구간마다 반전되는 마찰력의 부호변화를 고려하고, 이를 멱급수를 이용하여 전 구간으로 확장시킴으로써 쿨롱마찰을 고려한 단자유도계의 자유진동응답에 대해서 수학적으로 닫힌 해를 유도하였다. 또한, 마찰력의 크기가 강성에 의한 복원력의 크기보다 커지는 순간에 자유진동 운동이 정지하는 조건을 이용함으로써 주어진 초기조건에 대해서 예측되는 자유진동 반주기의 수와 운동이 정지하는 순간의 정확한 응답 값을 제안하였다.

대장내시경 전처치액으로서 Polyethylene Glycol용액과 Sulfate Free Polyethylene Glycol용액의 선호도에 관한 전향적 비교

이준석,박영숙,김남인,조윤주,김성환,송문희,전대원 대한소화기내시경학회 2009 Clinical Endoscopy Vol.38 No.5

Background/Aims: The standard polyethylene glycol (PEG) solution for colonic cleansing has a salty taste and a large volume of it is required, which can cause failure for the patient to ingest the required dosage. This has been a limitation for its usage. Sulfate free PEG (SF-PEG) has a less salty taste due to removal of the sodium sulfate, but the published studies in western countries about the preference and the degree of patient’s satisfaction with these two solutions has shown conflicting results. The object of this study was to compare SF-PEG with PEG solution in regard to preference, the degree of patient’s satisfaction and the adverse effects in Korean patients. We also attempted to determine whether these factors were associated with preference. Methods: Ninety-four patients scheduled for colonoscopy were given one liter of both solutions (SF-PEG and PEG) and then the patients were allowed to select either of the two solutions for the further two liters intake under informed consent. Before colonoscopy, the preferred solution, the degree of patient’s satisfaction, the adverse effects and other information were recorded by questionnaire. Results: Fifty-nine patients among the 94 patients (63%) preferred the SF-PEG solution (p<0.05). Especially, the young patients under the age of 35 preferred the SF-PEG solution (83% vs 58%; p=0.045), and patients who had already experienced colonoscopy with PEG solution tended to prefer the SF-PEG (54% vs 78%; p=0.054). Conclusions: Korean patients preferred the SF-PEG over PEG, and especially young aged patients and the patients who had already taken the PEG solution. Similar results were obtained for both solutions concerning the adverse effects, cleansing quality and compliance, and the degree of satisfaction was not much improved, which was probably due to the same large volume of fluid that is required for colon cleaning. 목적: Polyethylene glycol (PEG)용액은 정결효과가 우수하고, 안전하여 대장내시경 전처치액으로 널리 사용되고 있으나, 복용량이 많고, 고유의 짠맛으로 인하여 복용이 힘든 문제점이 있다. 1990년에 Sodium sulfate를 제거하여 짠맛을 줄인 sulfate free PEG (SF-PEG)용액이 개발되어 기존 PEG용액에 비해 복용 만족도, 순응도 및 부작용 등이 향상 될 것으로 생각되었다. 본 연구는 서양인과 다른 식이습관을 가진 한국인에서 기존 PEG용액과 SF-PEG용액간의 선호도, 만족도, 순응도, 부작용 및 장 정결도에 대해 비교하고, 선호도에 영향을 미치는 인자에 대해 알아보고자 하였다. 대상 및 방법: 을지대학교 노원을지병원에서 대장내시경을 시행한 환자 중 94명을 대상으로 모두에게 PEG와 SF-PEG용액 각각 1 L씩을 복용하게 한 후 나머지 2 L는 환자가 선택하여 복용하도록 하였다. 모든 대상자에서 선택한 전처치액을 조사 하였으며, 대장내시경 시행 전 설문지를 이용하여 만족도, 부작용, 남긴 양, 이전 대장내시경검사의 과거력 등에 대해 조사하였다. 복용 만족도는 visual analogue scale을 이용하여 평가하였으며, 대장내시경 시행 후 담당의가 대장 정결도에 대해 bad-fair-good-very good의 4단계로 나누어 평가 하였다. 결과: 총 94명중 SF-PEG용액을 선택한 환자가 59명으로(63%, p<0.05) 통계적으로 유의하게 선호도가 높았으며 복용 순서에 따른 차이는 없었다. 특히 35세 이하군에서 통계적으로 유의하게 SF-PEG용액을 더 선호하였다(83% vs. 58%, p=0.045). 이전 대장내시경 시행 당시 전처치액으로 PEG용액을 사용하였던 경험이 있는 군과 처음 대장내시경을 시행한 군을 비교하였을 때, 이전에 PEG용액을 복용하였던 군에서 SF-PEG용액을 더 선호하는 경향을 보였다(78% vs. 54%, p=0.054). 복용만족도, 부작용, 대장 정결도는 양군 간에 차이가 없었고 복용 순응도를 개선시키지는 못하였다. 결론: 본 연구에서는 대장내시경의 전처치액으로 기존 PEG용액에 비해 SF-PEG용액이 더 선호되는 것으로 조사되었으며, 특히 젊은 연령에서, 그리고 이전에 전처치액으로 PEG용액을 사용하였던 군에서 SF-PEG용액의 선호도가 더 높음을 알 수 있었으나 만족도와 순응도는 개선하지 못하였다.

핸드-아이 보정과 능동 스테레오 비젼의 일반적 해석

김진대(Jin-Dae Kim),이재원(Jeh-Woon Lee),신찬배(Chan-Bai Shin) Korean Society for Precision Engineering 2004 한국정밀공학회지 Vol.21 No.5

The analysis of relative pose(position and rotation) between stereo cameras is very important to determine the solution that provides three-dimensional information for an arbitrary moving target with respect to robot-end. In the space of free camera-model, the rotational parameters act on non-linear factors acquiring a kinematical solution. In this paper the general solution of active stereo that gives a three-dimensional pose of moving object is presented. The focus is to achieve a derivation of linear equation between a robot's end and active stereo cameras. The equation is consistently derived from the vector of quaternion space. The calibration of cameras is also derived in this space. Computer simulation and the results of error-sensitivity demonstrate the successful operation of the solution. The suggested solution can also be applied to the more complex real time tracking and quite general and are applicable in various stereo fields.

A Study on Separation Efficiency of the DNA-ELP Conjugates in Free-solution Capillary Electrophoresis using Unnatural Amino Acid Incorporation

Kyung-Ho SEO,Dong Hyun KIM,Jong-In WON 한국생물공학회 2015 한국생물공학회 학술대회 Vol.2015 No.4

Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory

Behera, Susanta,Kumari, Poonam Techno-Press 2018 Advances in computational design Vol.3 No.3

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

Free-edge effect in cross-ply laminated plates under a uniform extension

Sheng, Hongyu,Ye, Jianqiao Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.18 No.3

Based on the basic equations of elasticity, free-edge effects on stresses in cross-ply laminated plates are found by using the state space method. The laminates are subjected to uniaxial-uniform extension plate, which is a typical example of general plane strain problem. The study takes into account material constants of all individual material layers and the state equation of a laminate is solved analytically in the through thickness direction. By this approach, a composite plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The solution provides a continuous displacement and inter-laminar stress fields across all material interfaces and an approxiamte prediction to the singularity of stresses occurring in the boundary layer region of a free-edge. Numerical solutions are obtained and compared with the results obtained from an alternative numerical method.

Benchmark Modal Stress-Resultant Distributions for Vibrating Rectangular Plates with Two Opposite Edges Free

Y. Xiang,Wang, C.M.,T. Utsunomiya,C. Machimdamrong Computational Structural Engineering Institute of 2001 Computational structural engineering Vol.1 No.1

This paper presents exact solutions for the modal stress-resultant distributions for vibrating rectangular Mindlin plates involving two opposite sides simply supported while the other two sides free. These exact stress-resultants of vibrating plates with free edges, hitherto unavailable, are very important because they serve as benchmark solutions for checking numerical solutions and methods. Using the exact solutions of a square plate, this paper highlights the problem of determining accurate stress-resultants, especially the transverse shear forces and twisting moments in thin plates, when employing the widely used numerical methods such as the Ritz method and the finite element method. Thus, this study shows that there is a need for researchers to develop refinements to the Ritz method and the finite element method for determining very accurate stress-resultants in vibrating plates with free edges.

자유 라디칼 중합법을 활용한 CO₂ 기체분리용 PVA 기반 가지형 공중합체 복합막

박민수,김종학,라즈쿠마 파텔,Park, Min Su,Kim, Jong Hak,Patel, Rajkumar 한국막학회 2021 멤브레인 Vol.31 No.4

지구 온난화 이슈에서 가장 고질적인 문제 중 하나는 온실가스의 배출이다. 다양한 온실 가스 중 가장 높은 비중을 차지하는 이산화탄소(CO₂)는 이를 분리하기 위해 연구자들이 지속적으로 연구를 진행해오고 있다. 이러한 관점에서 본 연구에서는 이산화탄소 기체를 분리하기 위해 poly(vinyl alcohol) (PVA) 기반 공중합체를 제조하여 기체 분리막에 활용했다. 공중합체는 자유 라디칼 중합법을 활용했으며, 곁사슬을 위한 단량체로 아크릴산(acrylic acid)를 사용하여 PVA-g-PAA(VAA) 그래프트 공중합체를 제조했다. 본 공중합체를 이산화탄소 기체분리막에 적용한 사례는 최초이며, 폴리설폰 지지체에 복합막 형태로 제조했다. 공중합체 합성 결과는 FT-IR을 통해, 합성한 공중합체 의 거동은 TEM과 DSC, TGA를 통해 분석하였다. AA 그래프팅을 통해 공중합체는 나노 구조를 형성하며, PVA의 결정화도를 급격하게 감소시켜 이산화탄소의 용해도를 증가시켰고, 이는 이산화탄소 기체 분리 성능을 향상시켰다. 이를 통해 이산화탄소 분리막 분야에 용액-확산 및 그래프팅 방법이라는 새로운 접근법을 제시하였다. One of the chronic problems in the issue of global warming is the emission of greenhouse gases. Carbon dioxide (CO₂), which accounts for the highest proportion of various greenhouse gases, has been continuously researched by humans to separate it. From this point of view, a poly(vinyl alcohol) (PVA)-based copolymer with acrylic acid monomer was utilized in a gas separation membrane in this study. We employed a free radical polymerization to fabricate PVA-g-PAA (VAA) graft copolymer. It was utilized in the form of a composite membrane on a polysulfone substrate. The proper amount of acrylic acid reduced the crystallinity of PVA and increased CO₂ solubility in separation membranes. In this perspective, we suggest the novel approach in CO₂ separation membrane area by grafting and solution-diffusion.

Theory and technology of growing striation-free crystals

Scheel, Hans J. The Korea Association of Crystal Growth 2004 韓國結晶成長學會誌 Vol.14 No.4

Striations are growth-induced inhomogeneities which hamper the applications of solid-solution crystals and of doped crystals in numerous technologies. Thus the optimized performance of solid solutions often can not be exploited. The inhomogeneity problem can be solved in specific cases by achieving a distribution coefficient one in growth from melts and from solutions. Macrostep-induced striations can be suppressed by controlling the growth mode, by achieving growth on facets thereby preventing step bunching. Thermal striations are commonly assumed to be caused by convective instabilities so that reduced convection by microgravity or by damping magnetic fields was and is widely attempted to reduce such inhomogeneities. Here it will be shown that temperature fluctuations at the growth interface cause striations, and that hydrodynamic fluctuations in a quasi-isothermal growth system do not cause striations. The theoretically derived conditions were experimentally established and allowed the growth of striation-free crystals of $KTa_{1-x}Nb_xO_3$"KTN" solid solutions. Hydrodynamic variations from the accelerated crucible rotation technique ACRT did not cause striations as long as the temperature was controlled within $0.03^{\circ}$ at $1200^{\circ}C$ growth temperature. Alternative approaches to solve or reduce the segregation and striation problems in growth from melts and from solutions are discussed as well.

Exact solution for free vibration of curved beams with variable curvature and torsion

Zhu, Li-Li,Zhao, Ying-Hua,Wang, Guang-Xin Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.47 No.3

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.