• 한국해양공학회지
• /
• 제27권6호
• /
• pp.22-26
• /
• 2013

The purpose of this study was to improve the design of a mooring line by attaching a lumped mass to it on the seabed. A numerical analysis of the redesigned mooring system is performed to analyze the effect of the weight of the attached lumped mass using the commercial software Orcaflex. The ultimate tension of the mooring system with the lumped mass is compared with that of a bare mooring line in the original design. An appropriately designed weight for the lumped mass is found to induce a critical lifted point in the mooring line by floater motion in the ultimate condition to move toward the floater position from the anchor point, while maintaining a similar safety factor for the mooring line. On the other hand, it is shown that excess weight for the lumped mass induces snapping in a mooring line, resulting in low safety factor for the mooring system. The distance between lumped weights is shown to be a minor parameter affecting the safety of a mooring line, although a shorter line has an advantage from an economic point of view. Using the optimal weight for the lumped mass attached to the mooring line on a seabed reduces the mooring line length and installation area occupied by a mooring system under real sea conditions.

• 한국지진공학회논문집
• /
• 제23권4호
• /
• pp.231-238
• /
• 2019

A conventional lumped-mass stick model is based on the tributary area method to determine the masses lumped at each node and used in earthquake engineering due to its simplicity in the modeling of structures. However the natural frequencies of the conventional model are normally not identical to those of the actual structure. To solve this problem, recently an updated lumped-mass stick model is developed to provide the natural frequencies identical to actual structure. The present study is to investigate the seismic response accuracy of the updated lumped-mass stick model, comparing with the response results of the shaking table test. For the test, a small size four-story steel frame structure is prepared and tested on shaking table applying five earthquake ground motions. From the comparison with shaking table test results, the updated model shows an average error of 3.65% in the peak displacement response and 9.68% in the peak acceleration response. On the other hand, the conventional model shows an average error of 5.15% and 27.41% for each response.

• Structural Engineering and Mechanics
• /
• 제53권3호
• /
• pp.537-573
• /
• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• 한국지진공학회논문집
• /
• 제16권4호
• /
• pp.19-26
• /
• 2012

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 분석이나 지진 취약도 분석과 같은 방대한 지진데이터를 이용한 평가에서는 집중질량모델이 선호된다. 하지만 기존의 집중질량모델은 일반적으로 구조물의 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 단면을 갖는 기둥에 대해 동적해석을 수행하였다. 또한 감쇠비에 따른 동적성능을 분석하기 위해 1%에서 5%까지의 Rayleigh Damping 적용하여 그 결과를 유한요소모델 결과와 비교하였다.

• Structural Engineering and Mechanics
• /
• 제22권6호
• /
• pp.701-717
• /
• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• 한국소음진동공학회논문집
• /
• 제13권5호
• /
• pp.393-399
• /
• 2003

Hydraulic mounts show strong1y frequency-dependent stiffness and damping characteristics in low frequency range, which result from so called inertia track dynamics. A lumped mass has been incorporated in several mechanical models of the literature to take the inertia effect of the fluid in the track into consideration. Although complex s%illness by the mechanical model showed good agreements with the measured values, there exists a critical pitfall. In this paper, the shortcomings of mechanical models with lumped mass for hydraulic founts are clearly identified by illustrating actual measurements of the stiffness parameters for a hydraulic mount. It is conclusively discussed that the inertia effect of the fluid flow through the circular track is significant but latent. As an alternative to the mechanical model, a hydraulic model is claimed to be used for further dynamic analysis of engine/mount system or whole car system.

• 전산구조공학
• /
• 제10권3호
• /
• pp.217-223
• /
• 1997

본 논문은 집중 질량 구조물의 천이응답에 대한 시간영역 민감도 해석의 기본 개념을 설명한다. 외부 가진에 따른 구조물의 응답에 미치는 설계변수 변화의 영향을 구하기 위해 시간영역 민감도 함수를 구하는 방법을 제시하였다. 시간영역에서 구조물의 설계변수 민감도는 1차 표준 민감도 함수와 백분율 민감도 함수를 통해 확인하였다. 이러한 민감도 함수와 그 계산은 설계변수에 대한 시스템 상태변수의 편미분에 의한 것이다. 또한, 직접 미분법에 의한 해석적 방법의 편미분 결과와 수치적 방법에 의한 결과를 비교하였다.

• 한국해양공학회지
• /
• 제23권1호
• /
• pp.54-59
• /
• 2009

In this paper, the effect of the position and size of a lumped mass on the structural stability of a high speed underwater vehicle is presented. For simplicity, a real vehicle was modeled as a follower force subjected beam that was resting on an elastic foundation, and the lumped mass effect was simplified as an elastic intermediate support. The stability of the simplified model was numerically analyzed based on the Finite element method (FEM). This numerical simulation revealed that flutter type instability or divergence type instability occurs, depending on the position and stiffness of the elastic intermediate support, which implies that the instability of the real model is affected by the position and size of the lumped mass.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2008년도 춘계학술대회논문집
• /
• pp.389-392
• /
• 2008

This paper predicts the changes of natural frequencies due to the changes of mass at different point mass stations by using iterative calculation Transfer Matrices Method for different boundary conditions of a single beam structure (fixed-free and fixed-fixed beam). Firstly, the first three natural frequencies of an original beam are obtained using Transfer Matrices Method to verify the accuracy of the obtained results. The results are then compared with the exact solutions before purposely changing the parameter of mass. Both beams are modeled as discrete continuous systems with six-lumped-mass system. A single beam is broken down into a point mass and a massless beam which represent a single station and expressed in matrix form. The assembled matrices are used to determine the value of natural frequencies using numerical interpolation method corresponding to their mode number by manipulating some elements in the assembled matrix.

• 한국해양공학회지
• /
• 제33권5호
• /
• pp.400-410
• /
• 2019

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.