확장형 칼만필터를 이용한 현수교의 감쇠성능 평가

박동욱(Park Dong-Uk),김남식(Kim Nam-Sik) 대한토목학회 2011 대한토목학회논문집 A Vol.31 No.2A

감쇠비는 현수교에 있어서 교량진동을 평가하기 위한 중요한 동적 요소 중 하나이다. 하지만, 실재 현수교에서 계측된 상시 진동신호로부터 감쇠비를 직접적으로 추정하는 것은 현실적으로 매우 어려운 일이다. 뿐만 아니라, 한정된 계측자료를 이용하여 추정된 감쇠비로부터 공기역학적 감쇠와 마찰 감쇠를 구분하는 것은 더욱 어렵다. Macdonald는 2005년 발표한 자료에서 공기 역학적 감쇠성능은 풍속에 따라 선형적으로 증가한다고 하였으며, Park등은 감쇠성능은 진동의 크기에 따라 변화할 수 있다고 하였다. 따라서 본 논문에서는 이러한 감쇠비, 풍속, 진동의 크기 사이의 관계를 연구하여, 추정 감쇠비로부터 공기역학적 감쇠와 마찰 감쇠를 구분하고자 하였다. 본 논문에서 감쇠비 추정대상으로는 전라남도 고흥에 위치한 소록대교를 선택하였으며, 감쇠비 추정에는 Hilbert 변환법을 이용한 방법과 확장형 칼만필터를 이용하였다. 또한 두 방법으로 추정된 감쇠비들을 상호 비교를 실시하였다. 그 결과, 상시진동 자료와 차량재하실험으로부터 얻어진 자료를 이용하여 추정된 감쇠비와 풍속, 그리고 가속도의 크기를 이용하여 추정 감쇠비로부터 공기역학적 감쇠 성능과 마찰 감쇠 성능의 구분이 가능하다는 것을 알 수 있었다. The damping ratio as an index of bridge vibration could be considered as one of the important dynamic characteristics of a suspension bridge. But estimating of damping ratio on an existing suspension bridge under ambient vibration condition could be a laborious task. Moreover, it is not simple to directly distinguish aerodynamic damping and friction damping from apparent damping. According to previous studies, the aerodynamic damping properties can be linearly affected by wind speed level, and apparent damping ratio can be affected by amplitude of vibration. Therefore, in this article, the relationships among damping ratio, wind speed level and amplitude of acceleration were studied for separating extract aerodynamic damping and friction damping from apparent damping. Damping ratios on Sorok Bridge, a suspension bridge which is a located in Go-Heung, Korea, were estimated by two different methods as using Hilbert transform and extended Kalman filter which were well known as effective estimation methods for non-linear state. It was possible to distinguish aerodynamic damping and friction damping from apparent damping using averaged normal components of wind speed, RMQ values of acceleration, and estimated damping ratios from wind-induced vibration responses and vehicle loading responses.

Wind-induced conductor response considering the nonproportionality of generalized aerodynamic damping

Wenjuan Lou,Dengguo Wu,Haiwei Xu 대한기계학회 2019 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.33 No.7

Aerodynamic damping is a key factor that influences the wind-induced responses of transmission conductors. The inaccurate estimation of aerodynamic damping leads to misunderstanding of conductor response to wind actions. For dynamic response analysis in the frequency domain, the generalized aerodynamic damping matrix used to solve conductor motion is diagonal. This study reanalyzed the conductor generalized aerodynamic damping matrix by considering its horizontal and vertical motions and the coupling effects of different modes. The derived generalized aerodynamic damping was a nondiagonal matrix, and we defined it as nonproportional generalized aerodynamic damping. Variations in the aerodynamic damping ratio and the nonproportionality of generalized aerodynamic damping with wind speed were investigated through numerical studies of single- and triple-span conductors. Triple-span conductors with different span lengths, hanging heights, and initial pretension forces were adopted to discuss the effects of the nonproportionality of generalized aerodynamic damping on estimating the dynamic responses of conductors. Results showed that neglecting the vertical motion of a conductor leads to an overestimation of the aerodynamic damping ratio, especially under high wind speed conditions. The nonproportionality of generalized aerodynamic damping is highest when the incoming wind speed at 10 m is 25 m/s. Ignoring such nonproportionality leads to an overestimation of the resonant responses of conductors but exerts minimal effects on total fluctuating responses mainly contributed by background components. Therefore, for a transmission conductor with a significant resonant response, the nonproportionality effect of generalized aerodynamic damping must be considered. Increasing span length and conductor height or reducing initial pretension force seems to enhance nonproportionality effects on conductor responses.

ON ANALYTICAL SOLUTION OF NON LINEAR ROLL EQUATION OF SHlPS

S. Rao TATA,Kuniaki SHOJI,Shigeo MITA,Kiyokazu MINAMI 한국항해항만학회 2006 한국항해항만학회 학술대회논문집 Vol.2006 No.-

Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. There are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained from forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are composed with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

Structural Damping Effects on Stability of a Cantilever Column under Sub-tangentially Follower Force

Dong-Ju Min(민동주),Jae-gyun Park(박재균),Moon-Young Kim(김문영) 한국소음진동공학회 2016 한국소음진동공학회 학술대회논문집 Vol.2016 No.4

A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.

Experimental study of vibration characteristics of FRP cables based on Long-Gauge strain

Qi Xia,JiaJia Wu,XueWu Zhu,Jian Zhang 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.63 No.6

Steel cables as the most important components are widely used in the certain types of structures such as cablesupported bridges, but the long-span structures may result in an increase in fatigue under high stress and corrosion of steel cables. The traditional steel cable is becoming a more evident hindrance. Fiber Reinforced Polymer (FRP) cables with lightweight, high-strength are widely used in civil engineering, but there is little research in vibrational characteristics of FRP cables, especially on the damping characteristic. This article studied the two methods to evaluate dynamical damping characteristic of basalt FRP(BFRP) and glass FRP(GFRP) cables. First, the vibration tests of the B/G FRP cables with different diameter and different cable force were executed. Second, the cables forces were calculated using dynamic strain, static strain and dynamic acceleration respectively, which were further compared with the measured force. Third, experimental modal damping of each cables was calculated by the half power point method, and was compared with the calculation by Rayleigh damping theory and energy dissipation damping theory. The results indicate that (1) The experimental damping of FRP cables decreases with the increase of cable force, and the trend of experimental damping changes is roughly similar with the theoretical damping. (2) The distribution of modal damping calculated by Rayleigh damping theory is closer to the experimental results, and the damping performance of GFRP cables is better than BFRP cables.

등가점성감쇠법을 이용한 배관곡관요소 비선형 거동의 감쇠효과 분석

이창균(ChangKyun Lee),이은호(EunHo Lee),임진우(JinWoo Im),라치웅(ChiWoong La),박노철(No-Cheol Park) 대한기계학회 2021 대한기계학회 춘추학술대회 Vol.2021 No.4

설계 초과지진하중에 대한 변형률 기반 평가방법 도입에 대한 연구가 활발하게 이루어지는 가운데, 비선형거동 확인을 위해서 유한요소 해석방법을 주로 이용하고 있다. 이에 따라 소성이 발생하였을 때의 감쇠효과에 대한 분석방법이 필요하게 되었다. 기존 탄성 영역에서 수행되던 유한요소해석에서는 영구변형에 따른 에너지 소산효과가 존재하지 않기 때문에 시스템 구조 자체에서 발생하는 감쇠효과를 보수적으로 고려하는 방법을 차용하였다. 하지만 변형이 발생하는 비선형해석에서는 시스템 구조 자체의 감쇠율 뿐 아니라 영구변형, 즉 소성변형에 따른 에너지 소산율도 고려되기 때문에 적절한 감쇠율 적용에 대한 고찰이 필요하다. 본 연구에서는 유한요소해석 모델에서 등가점성감쇠법을 이용하여 비선형거동을 하는 배관요소의 감쇠효과를 분석하고, 이를 활용한 유한요소해석에서의 적용 방안에 대해서 연구해보았다. 등가점성감쇠법이란, 선형 시스템에 감쇠율을 적용하여 비선형 응답을 예측하기 위해 적용되던 방식으로, 대표적으로 Jenning 의 연구를 통해 단자유도계 시스템의 비선형 거동을 예측하는 방법으로 3 가지 관점이 제시되었다.⁽¹⁾ 또한 등가점성감쇠법은 DDBD(Direct Displacement-Based Design) 방법을 활용하여 실제 구조물의 비선형응답을 예측하는 방법론으로 정리된 바 있다.⁽²⁾ 고찰을 위해 유한요소해석법을 이용하여 곡관 시스템의 탄소성해석의 결과를 바탕으로 Effective Stiffness 와 Effective Natural Frequency 를 계산하는 방법을 제시하고, 이를 활용하여 등가점성감쇠율을 계산하였다. 해당 방법을 곡관 요소의 파손실험결과에 활용하여 등가점성감쇠율을 활용한 곡관의 비선형 거동 예측 가능성을 확인할 수 있을 것으로 기대된다. In the process of studying on introduction of strain-based evaluation methods for BDBE(Beyond Design Basis Earthquake) Conditions are actively conducted, finite element analysis methods are commonly used to confirm. Accordingly, it is necessary to analyze damping effect. In the existing evaluation, since energy dissipation effect due to plastic deformation does not exist, a method of conservatively considering the damping effect occurring in the system structure itself was adopted. However, in nonlinear domain, in which deformation occurs, not only damping rate of the system structure itself, but also energy dissipation due to plastic deformation are considered, so it is necessary to consider appropriate damping. In this study, the damping effect of nonlinear curved pipe element using the equivalent viscous damping method was analyzed by finite element analysis and studied the application of this method. Equivalent viscosity damping method is applied to predict the nonlinear response by applying a damping factor to a linear system, and representatively, through Jenning's research, three viewpoints were presented as a method of predicting the nonlinear behavior of SDOF system.⁽¹⁾ In addition, the equivalent viscous damping method summarized as a methodology for predicting the nonlinear response of actual structure using Direct Displacement-Based Design (DDBD) method.⁽²⁾ For consideration, a method of calculating Effective Stiffness and Effective Natural Frequency based on the results of the elasto-plastic analysis of a curved pipe system using finite element analysis was presented, and the equivalent viscous damping ratio was calculated using this method. It is expected that the feasibility of predicting the nonlinear behavior of the curved pipe using the equivalent viscous damping method can be confirmed by the failure test results.

Analytical and numerical algorithm for exploring dynamic response of non-classically damped hybrid structures

Raheem, Shehata E. Abdel Techno-Press 2014 Coupled systems mechanics Vol.3 No.2

The dynamic characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of hybrid structure with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as can mass and stiffness. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. A numerical algorithm capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to explore the dynamic response of hybrid tower of cable-stayed bridges: The first approach makes use of a simplified model of 2 coupled lumped masses to investigate the effects of subsystems different damping, mass ratio, frequency ratio on dynamic characteristics and equivalent modal damping; the second approach employs a detailed numerical step-by step integration procedure.

Dynamic behavior of intake tower considering hydrodynamic damping effect

Md Ikram Uddin,Tahmina Tasnim Nahar,Dookie Kim,Kee-Dong Kim 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.82 No.3

The effect of hydrodynamic damping on intake tower is twofold: one is fluid damping and another is structural damping. Fluid damping can be derived analytically from the governing equation of the fluid-structure-interaction (FSI) problem which yields a very complicated solution. To avoid the complexity of the FSI problem water-tower system can be simplified by considering water as added mass. However, in such a system a reconsideration of structural damping is required. This study investigates the effects of this damping on the dynamic response of the intake tower, where, apart from the “no water (NW)” condition, six other cases have been adopted depending on water height. Two different cross-sections of the tower are considered and also two different damping properties have been used for each case as well. Dynamic analysis has been carried out using horizontal ground motion as input. Finally, the result shows how hydrodynamic damping affects the dynamic behavior of an intake tower with the change of water height and cross-section. This research will help a designer to consider more conservative damping properties of intake tower which might vary depending on the shape of the tower and height of water.

스트레인 에너지를 이용한 제진재 위치 결정

김중배(Kim, Joong-Bae),유국현(Ryu, Kuk-Hyun),박상규(Park, Sang-Kyu),이상조(Lee, Sang-Jo) 한국소음진동공학회 2008 한국소음진동공학회 논문집 Vol.18 No.11

The vehicle design engineers have studied the method of applying damping materials to the vehicle bodies by computer simulations and experimental methods in order to improve the vibration and noise characteristics of the vehicles. The unconstrained layer damping, being concerned with this study, has two layers(base layer and damping layer) and proyides vibration control of the base layer through extensional damping. Generally this kind of surface damping method is effectively used in reducing structural vibration at frequencies beyond 150Hz. The most important thing is how to apply damping treatment with respect to location and size of the damping material. To solve these problems, the current experimental methods have technical limits which are cumbersome, time consuming, and expensive. This Paper proposes a method based on finite element method and it employes averaged ESE(element strain energy) percent of total of dash panel assembly for 1/1 octave band frequency range by MSC/NASTRAN. The regions of high ESE percent of total are selected as proposed location of damping treatment. The effect of damping treatment is analyzed by comparing the frequency response function of the SPCC bare Panel and the damping treated panels.

Estimation of NonlinearSite Effects of Soil Profiles in Korea

이홍성,윤세웅,박두희,김인태 한국지반공학회 2008 한국지반공학회논문집 Vol.24 No.3

In a nonlinear site response analysis which is performed in time domain, small strain damping is modeled as viscous damping through use of various forms of Rayleigh damping formulations. Small strain damping of soil is known to be independent of the loading frequency, but the viscous damping is greatly influenced by the loading frequency. The type of Rayleigh damping formulation has a pronounced influence on the dependence. This paper performs a series of nonlinear analyses to evaluate the degree of influence of the viscous damping formulation on Korean soil profiles. Analyses highlight the strong influence of the viscous damping formulation for soil profiles exceeding 30 m in thickness, commonly used in simplified Rayleigh damping formulation overestimating energy dissipation at high frequencies due to artificially introduced damping. When using the full Rayleigh damping formulation and carefully selecting the optimum modes, the artificial damping is greatly reduced. Results are further compared to equivalent linear analyses. The equivalent linear analyses can overestimate the peak ground acceleration even for shallow profiles less than 20 m in thickness.