• Title/Summary/Keyword: 진동방정식

Search Result 658, Processing Time 0.024 seconds

Dynamical Analysis of the Mooring Vessel System Under Surge Excitations (선박 계류시스템의 종방향 외력하의 비선형 동적거동 해석)

  • Lee, Sang-Do;You, Sam-Sang
    • Journal of the Korean Society of Marine Environment & Safety
    • /
    • v.24 no.2
    • /
    • pp.140-145
    • /
    • 2018
  • This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.

A Numerical Simulation of Three- Dimensional Nonlinear Free surface Flows (3차원 비선형 자유표면 유동의 수치해석)

  • Chang-Gu Kang;In-Young Gong
    • Journal of the Society of Naval Architects of Korea
    • /
    • v.28 no.1
    • /
    • pp.38-52
    • /
    • 1991
  • In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

  • PDF

Finite Element Analysis for Evaluation of Viscous and Eccentricity Effects on Fluid Added Mass and Damping (유체 부가질량 및 감쇠 결정시 점성 및 편심 영향에 대한 유한요소해석)

  • 구경회;이재한
    • Journal of the Earthquake Engineering Society of Korea
    • /
    • v.7 no.2
    • /
    • pp.21-27
    • /
    • 2003
  • In general, simple fluid added mass method is used for the seismic and vibration analysis of the immersed structure to consider the fluid-structure interaction effect. Actually, the structural response of the immersed structure can be affected by both the fluid added mass and damping caused by the fluid viscosity. These variables appeared as a consistent matrix form with the coupling terms. In this paper, finite element formula for the inviscid fluid case and viscous fluid case are derived from the linearized Navier Stoke's equations. Using the finite element program developed in this paper, the analyses of fluid added mass and damping for the hexagon core structure of the liquid metal reactor are carried out to investigate the effect of fluid viscosity with variation of the fluid gap and Reynolds number. From the analysis results, it is verified that the viscosity significantly affects the fluid added mass and damping as the fluid gap size decrease. From the analysis results of eccentricity effect on the fluid added mass and damping of the concentric cylinders, the fluid added mass increase as the eccentricity increases, however the fluid damping increases only when the eccentricity is very severe.

Real-time Hybrid Testing a Building Structure Equipped with Full-scale MR dampers and Application of Semi-active Control Algorithms (대형 MR감쇠기가 설치된 건축구조물의 실시간 하이브리드 실험 및 준능동 알고리즘 적용)

  • Park, Eun-Churn;Lee, Sung-Kyung;Lee, Heon-Jae;Moon, Suk-Jun;Jung, Hyung-Jo;Min, Kyung-Won
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.21 no.5
    • /
    • pp.465-474
    • /
    • 2008
  • The real-time hybrid testing method(RT-HYTEM) is a structural testing technique in which the numerical integration of the equation of motion for a numerical substructure and the physical testing for an experimental substructure are performed simultaneously in real-time. This study presents the quantitative evaluation of the seismic performance of a building structure installed with an passive and semi-active MR damper by using RT-HYTEM. The building model that was identified from the force-vibration testing results of a real-scaled 5-story building is used as the numerical substructure, and an MR damper corresponding to an experimental substructure is physically tested by using the universal testing machine(UTM). The RT-HYTEM implemented in this study is validated because the real-time hybrid testing results obtained by application of sinusoidal and earthquake excitations and the corresponding analytical results obtained by using the Bouc-Wen model as the control force of the MR damper respect to input currents were in good agreement. Also for preliminary study, some semi-active control algorithms were applied to the MR damper in order to control the structural responses optimally. Comparing between the test results of semi-active control using RT-HYTEM and numerical analysis results show that the RT-HYTEM is more resonable than numerical analysis to evaluate the performance of semi-active control algorithms.

Seismic Performance Evaluation of a Cone-type Friction Pendulum Bearing System (원추형 마찰진자베어링의 내진성능평가)

  • Jeon, Bub-Gyu;Chang, Sung-Jin;Park, Kyung-Rock;Kim, Nam-Sik;Jung, Duk-Young
    • Journal of the Earthquake Engineering Society of Korea
    • /
    • v.15 no.2
    • /
    • pp.23-33
    • /
    • 2011
  • In this study, a CFPBS (Cone-type Friction Pendulum Bearing System) was developed which controls the acceleration delivered to the structure to prevent damage and degradation of the critical communication equipment in case of an earthquake. The isolation performance of the CFPBS was evaluated by numerical analysis. The CFPBS was manufactured in the shape of a cone differenced from the existing FPS (Friction Pendulum System), and a pattern was engraved on the friction surface. The natural frequencies of the CFPBS were evaluated from a free-vibration test with the seismic isolator system consisting of four CFPBSs. In order to verify its earthquake-resistant performance, a numerical analysis program was created from the equation of the CFPBS induced from the equations of motion. A simplified theoretical equation of the CFPBS was proposed to manufacture the equipment which could demonstrate the necessary performance. Artificial seismic waves satisfying the maximum earthquake scale of the Korean Building Code-Structural (KBC-2005) were created and verified to review the earthquake-resistant performance of the CFPBS by numerical analysis. The superstructural mass of the CFPBS and skew angle of the friction surface were considered for numerical analysis with El Centro NS (1940), Kobe NS (1995) and artificial seismic waves. The CFPBS isolation performance evaluation was based on the results of numerical analysis and the executed comparative analysis between the results from numerical analysis and the simplified theoretical equation under the same conditions.

Study on the Non-isothermal Crystallization Kinetics of Branched Polypropylene (분지형 폴리프로필렌의 비등온결정화 거동 연구)

  • Yoon, Kyung-Hwa;Shin, Dong-Yup;Kim, Youn-Cheol
    • Polymer(Korea)
    • /
    • v.36 no.2
    • /
    • pp.245-250
    • /
    • 2012
  • Branched polypropylenes (PP) with long chain branch were prepared by solid state reaction with three different branching agent of 0.3 wt% content. The chemical structures, non-isothermal crystallization behavior and complex viscosity of the branched PP were investigated by FTIR, DSC, optical microscope, and dynamic rheological measurement. The chemical structure of the branched PP was confirmed by the existence of =C-H stretching peak of the branching agent at 3100 $cm^{-1}$. There was no distinct change in melting temperature in case of PP-D-0-3 and PP-F-0-3, but PP-H-0-3 indicated a decrease in melting temperature. The decrease in melting temperature was interpreted by the fact that the degradation reaction of PP was more dominant than branched reaction, and confirmed by a decrease in complex viscosity. The non-isothermal crystallization behavior of the branched PP was analyzed using by Avrami equation. The Avrami exponent of PP was 3, and the values of the branched PP with DVB and FS were below 3. The activation energy of PP calculated by Kissinger method was 25 kJ/mol, and there were no big difference in activation energies of the branched PPs compared to PP.

Development of Three-dimensional Inversion Algorithm of Complex Resistivity Method (복소 전기비저항 3차원 역산 알고리듬 개발)

  • Son, Jeong-Sul;Shin, Seungwook;Park, Sam-Gyu
    • Geophysics and Geophysical Exploration
    • /
    • v.24 no.4
    • /
    • pp.180-193
    • /
    • 2021
  • The complex resistivity method is an exploration technique that can obtain various characteristic information of underground media by measuring resistivity and phase in the frequency domain, and its utilization has recently increased. In this paper, a three-dimensional inversion algorithm for the CR data was developed to increase the utilization of this method. The Poisson equation, which can be applied when the electromagnetic coupling effect is ignored, was applied to the modeling, and the inversion algorithm was developed by modifying the existing algorithm by adopting comlex variables. In order to increase the stability of the inversion, a technique was introduced to automatically adjust the Lagrangian multiplier according to the ratio of the error vector and the model update vector. Furthermore, to compensate for the loss of data due to noisy phase data, a two-step inversion method that conducts inversion iterations using only resistivity data in the beginning and both of resistivity and phase data in the second half was developed. As a result of the experiment for the synthetic data, stable inversion results were obtained, and the validity to real data was also confirmed by applying the developed 3D inversion algorithm to the analysis of field data acquired near a hydrothermal mine.

Can We Hear the Shape of a Noise Source\ulcorner (소음원의 모양을 들어서 상상할 수 있을까\ulcorner)

  • Kim, Yang-Hann
    • Transactions of the Korean Society for Noise and Vibration Engineering
    • /
    • v.14 no.7
    • /
    • pp.586-603
    • /
    • 2004
  • One of the subtle problems that make noise control difficult for engineers is “the invisibility of noise or sound.” The visual image of noise often helps to determine an appropriate means for noise control. There have been many attempts to fulfill this rather challenging objective. Theoretical or numerical means to visualize the sound field have been attempted and as a result, a great deal of progress has been accomplished, for example in the field of visualization of turbulent noise. However, most of the numerical methods are not quite ready to be applied practically to noise control issues. In the meantime, fast progress has made it possible instrumentally by using multiple microphones and fast signal processing systems, although these systems are not perfect but are useful. The state of the art system is recently available but still has many problematic issues : for example, how we can implement the visualized noise field. The constructed noise or sound picture always consists of bias and random errors, and consequently it is often difficult to determine the origin of the noise and the spatial shape of noise, as highlighted in the title. The first part of this paper introduces a brief history, which is associated with “sound visualization,” from Leonardo da Vinci's famous drawing on vortex street (Fig. 1) to modern acoustic holography and what has been accomplished by a line or surface array. The second part introduces the difficulties and the recent studies. These include de-Dopplerization and do-reverberation methods. The former is essential for visualizing a moving noise source, such as cars or trains. The latter relates to what produces noise in a room or closed space. Another mar issue associated this sound/noise visualization is whether or not Ivecan distinguish mutual dependence of noise in space : for example, we are asked to answer the question, “Can we see two birds singing or one bird with two beaks?"