전차선 집중질량 모델과 분포질량 모델의 비교 해석

오성택(SeongTaek Oh),김백(Baik Kim) 한국철도학회 2013 한국철도학회 학술발표대회논문집 Vol.2013 No.11

주행 중인차량의 팬터그래프와 전차선 사이의 접촉력 또는 전차선의 압상량을 구하기 위해 전차선을 모델링하는 경우에 일반적으로는 가선계의 복잡한 요소들을 모델에 반영시키기 쉬운 집중질량 모델을 사용하고 있다. 집중질량 모델의 경우에는 질량점 간의 간격을 축소시키는 경우 분포질량 모델에 근접하게 되나 상태방정식의 수가 증가하여 계산시간이 오래 소요되거나 수치적분과정에서의 오차가 증가하게 된다. 본 연구에서는 단순현으로 표현된 전차선 분포질량 모델의 일반해를 그린 함수를 사용하여 구하고 이를 질량점 간격을 변화시킨 집중질량 모델에서의 결과와 비교하여 계산 시간과 정확도에서 수월성을 유지할 수 있는 질량점 간격을 도출해 내고자 한다. When we simulate the railway catenary systems to find out the contact force between the trolley wire and the running pantograph or uplift displacement of the trolley wire, the lumped mass model is widely used for its convenience of applying the complicated elements of the catenary systems to the model. Decreasing the distance between the lumped masses tends to approach the distributed model but increases the dimension of the states equation, which results in escalated numerical error and extended calculating time. In this study, we have found the general solution of the distributed model by exploiting the Green’s function and compared the results from the lumped model with altering the distance between masses to deduce the appropriate distance which maintains the excellency of calculating time and the accuracy.

구조물의 동적 고유특성을 이용한 새로운 집중질량모델 개발

노화성,윤지만,이후석,이종세 한국지진공학회 2012 한국지진공학회논문집 Vol.16 No.4

구조물의 내진설계 또는 내진성능평가를 위해서는 구조물의 축소모형을 이용한 실험적 분석이나 유한요소모델을 기반으로 한 수치적 방법이 고려된다. 수치적 방법을 위해서는 정교한 모델링이 요구될 경우 3차원 유한요소해석을 실시하나 민감도 분석이나지진 취약도 분석과 같은 방대한 지진데이터를 이용한 평가에서는 집중질량모델이 선호된다. 하지만 기존의 집중질량모델은 일반적으로구조물의 기하학적 형상을 고려하여 집중질량을 산출하는 방식인데, 이 경우 제공되는 고유치는 실구조물의 고유치와 일치하지 않는다.본 연구에서는 이러한 문제점을 개선하고 실구조물과 유사한 동적 거동을 발현하는 새로운 형식의 주파수 순응형 집중질량모델을 제안하였다. 제안된 모델은 실구조물의 고유치와 고유 벡터, 모드 형상 등을 고려하여 생성하며, 모델의 성능을 검증하기 위해 비균일 단면을갖는 기둥에 대해 동적해석을 수행하였다. 또한 감쇠비에 따른 동적성능을 분석하기 위해 1%에서 5%까지의 Rayleigh Damping 적용하여 그 결과를 유한요소모델 결과와 비교하였다. For a seismic design or performance evaluation of a structure, an experimental investigation on a scale model of the structure or numerical analysis based on the finite element model is considered. Regarding the numerical analysis, a three-dimensional finite element analysis is performed if a high accuracy of the results is required, while a sensitivity or fragility analysis which uses huge seismic ground motions leads to the use of a lumped-mass stick model. The conventional modeling technique to build the lumped-mass stick model calculates the amount of the lumped mass by considering the geometric shape of the structure, like a tributary area. However, the eigenvalues of the conventional model obtained through such a calculation are normally not the same as those of the actual structure. In order to overcome such a deficiency, in this study, a new lumped mass stick model is proposed. The model is named the “frequency adaptive-lumped-mass stick model.” It provides the same eigenvalues and similar dynamic responses as the actual structure. A non-prismatic column is considered as an example, and its natural frequencies as well as the dynamic performance of the new lumped model are compared to those of the full-finite element model. To investigate the damping effect on the new model, 1% to 5% of the critical damping ratio is applied to the model and the corresponding results are also compared to those of the finite element model.

비보존력을 받는 다수의 집중질량을 갖는 외팔보의 안정성에 관한 연구

노광춘,박영필 대한기계학회 1986 대한기계학회논문집 Vol.10 No.1

본 연구에서는 종등력을 받는 다수의 집중질량을 갖는 외팔보에 대해 집중질 량의 위치, 집중질량간의 집중질량비 및 집중질량대 분포질량의 질량비에 따른 보의 안정성에 관해 연구하였다. The stability behavior of the cantilever beam carrying several masses and subjected to a follower force at its free end is investigated. The effects of the location and the mass ratio of the concentrated masses on the stability of the system are discussed. An optimal location of the concentrated mass is determined to give maximum critical follower force. Discontinuities of the flutter load are observed for the system with more than two concentrated masses.

집중질량을 고려한 보강된 사다리꼴 주름판의 진동해석

정강(Kang Jung),김영완(Young-Wann Kim) 한국소음진동공학회 2014 한국소음진동공학회 논문집 Vol.24 No.5

집중질량을 갖는 변단면 보강 후판의 자유진동해석

이용수(Lee, Yong-Soo),김일중(Kim, Il-Jung),오숙경(Oh, Soog-Kyoung) 한국소음진동공학회 2009 한국소음진동공학회 논문집 Vol.19 No.8

Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on elastic foundation(in a case of pasternak foundation or winkler foundation). And there are many machines in sub-structures of buildings and slabs of sub-structures are affected by vibration which they make. This paper deals with vibration of plates on elastic foundation. Machines on plates are considered as concentrated mass. This paper has the object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate with Concentrated Masses in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. The Winkler parameter is varied with 10, $10^2$, $10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0. And the Concentrated Mass is applied as P1, Pc, P2 respectively.

진동대 실험을 통한 업데이트된 집중질량스틱모델의 성능 비교

선휘창(Sun, Hwichang),노화성(Roh, Hwasung) 대한토목학회 2017 대한토목학회 학술대회 Vol.2017 No.10

집중 질량을 가진 회전하는 외팔 평판의 진동 해석

양정식,유홍희 한국소음진동공학회 1998 소음 진동 Vol.8 No.6

A modelling method for the vibration analysis of rotating cantilever plates with a concentrated mass is presented. The equations of motion for the rotating plates with a concentrated mass located in an arbitrary position are derived and transformed into a dimensionless form. For the mathematical modelling of the concentrated mass. a mass density Dirac delta function is used. The effects of concentrated mass and its location. angular speed. plate aspect ratio. and hub radius of the rotating plate on the natural frequencies are studied. Particularly. mode shape variations due to some parameter variations are investigated.

유한요소모델의 모드참여계수를 이용한 집중질량스틱모델 개선

김태현 ( Kim Taehyeon ),이창석 ( Lee Changseok ),노화성 ( Roh Hwasung ) 한국구조물진단유지관리공학회 2020 한국구조물진단유지관리공학회 학술발표대회 논문집 Vol.24 No.1

실 구조물의 동적응답과 Correction Matrix를 도입한 개선된 LMS모델의 동적응답을 비교하였을 때 기존의 LMS 모델 보다는 동적응답의 정확도는 향상되었지만 여전히 최대동적응답에서는 다소 오차가 존재하였다. 이를 개선하기 위해 본 논문에서는 Correction Matrix에서 사용된 모드형상과 모드참여계수(modal participation factor)를 실구조물(FEM)의 모드참여계수와 관심위치에서의 모드형상 값으로 적용하였다. 대상 구조물은 4m 높이의 기둥이며 시간이력해석결과 시간이력 뿐만 아니라 최대 가속도 및 변위 응답 모두 동일하게 나타났다.

집중질량과 초기 비틀림각을 갖는 회전블레이드의 진동해석

곽주영,유홍희,Kwak, Joo-Young,Yoo, Hong-Hee 대한기계학회 1998 大韓機械學會論文集A Vol.22 No.1

Equations of motions of a pretwisted rotating blade with a concentrated mass in an arbitrary position are derived. The flapwise and chordwise equations are coupled to each other due to the pretwist angle of the blade. As the angular speed, hub radius ratio, pretwist angle and concentrated mass vary, the vibration characteristics of the blade change. It is found that eigenvalue lociveering phenomena occur between two closing loci due to the pretwist angle. The effect of the pretwist angle on the critical angular speed and location of the concentrated mass on the natural frequencies are also investigated.

집중질량 라인모델을 이용한 Steel Lazy Wave Riser의 비선형 동적 해석

오승훈,정재환,박병원,권용주,정동호 한국해양공학회 2019 韓國海洋工學會誌 Vol.33 No.5

In this study, the numerical code for the 3D nonlinear dynamic analysis of an SLWR (Steel Lazy Wave Riser) was developed using the lumped mass line model in a FORTRAN environment. Because the lumped mass line model is an explicit method, there is no matrix operation. Thus, the numerical algorithm is simple and fast. In the lumped mass line model, the equations of motion for the riser were derived by applying the various forces acting on each node of the line. The applied forces at the node of the riser consisted of the tension, shear force due to the bending moment, gravitational force, buoyancy force, riser/ground contact force, and hydrodynamic force based on the Morison equation. Time integration was carried out using a Runge–Kutta fourth-order method, which is known to be stable and accurate. To validate the accuracy of the developed numerical code, simulations using the commercial software OrcaFlex were carried out simultaneously and compared with the results of the developed numerical code. To understand the nonlinear dynamic characteristics of an SLWR, dynamic simulations of SLWRs excited at the hang-off point and of SLWRs in regular waves were carried out. From the results of these dynamic simulations, the displacements at the maximum bending moments at important points of the design, like the hang-off point, sagging point, hogging points, and touch-down point, were observed and analyzed.