• 한국전산구조공학회논문집
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• 제30권4호
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• pp.329-334
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• 2017

다양한 산업 분야의 구조물은 여러 부구조의 조합으로 구성되며, 시스템의 자유도 또한 무수히 많다. 높은 복잡성을 가지는 구조물의 해석 및 계산 효율을 향상시키기 위해서 해석 모델의 단순화 및 자유도 축소가 요구된다. 지난 50여 년 동안 규모가 큰 공학적 문제를 단순화하기 위해 다양한 부분구조화 기법들이 개발되어 왔다. 이러한 부분구조화 기법들은 Newton-Raphson 알고리즘 등과 같은 반복계산을 동반하는 비선형 구조해석 문제 해석에 매우 효과적이다. 본 논문에서는 기 개발된 비선형 부분구조화 기법 중의 하나인 모드미분(modal derivatives)을 이용하여 기하비선형 보의 모델 축소에 적용하고자 한다. 모드미분은 모드 기반 축소 기저의 2차항의 형태로, 선형모드의 조합으로 근사 가능한 변위벡터를 미소변위에 대한 Taylor 급수를 통해 확인할 수 있으며, 시스템의 고유치 문제를 모드 좌표로 미분을 함으로써 얻어진다. 모드미분에는 비선형 접선 강성행렬의 미분을 포함하고 있으며, 이는 유한차분법 등의 근사를 통해 계산할 수 있다. 제안된 방법론은 기하학적 비선형 문제에 우수한 성능을 보이는 동시회전 유한요소법에 적용하였다. 수치예제를 통해 보의 경계가 수평으로 움직일 수 있는 문제에서는 기존의 모드축소기법이 매우 비효율적임을 알 수 있었다. 한편 모드미분을 이용한 축소기법은 다양한 경계조건에 대하여 우수한 성능을 보임을 확인하였다.

• Structural Engineering and Mechanics
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• 제4권3호
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Wind and Structures
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• 제7권3호
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• pp.173-186
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• 2004

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. In this paper, one popular stochastic system identification technique, covariance-driven Stochastic Subspace Identification(SSI in short), is firstly presented for estimation of the flutter derivatives of bridge decks from their random responses in turbulent flow. Secondly, wind tunnel tests of a streamlined thin plate model and a ${\Pi}$ type blunt bridge section model are conducted in turbulent flow and the flutter derivatives are determined by SSI. The flutter derivatives of the thin plate model identified by SSI are very comparable to those identified by the unifying least-square method and Theodorson's theoretical values. As to the ${\Pi}$ type section model, the effect of turbulence on aerodynamic damping seems to be somewhat notable, therefore perhaps the wind tunnel tests for flutter derivative estimation of those models with similar blunt sections should be conducted in turbulent flow.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2001년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2001
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• pp.125-130
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• 2001

It is well known that many real systems have asymmetric mass, damping and stiffness matrices. In this case, the method for calculating eigenpair sensitivity is different from that of symmetric system. To determine the derivatives of the eigenpairs in asymmetric damped case, a modal method was recently developed by Adhikari. When a dynamic system has many degrees of freedom, only a few lower modes are available, and because the higher modes should be truncated to use the modal method, the errors may become significant. In this paper a procedure for determining the sensitivities of the eigenpairs of asymmetric damped system using a few lowest set of modes is proposed. Numerical examples show that proposed method achieves better calculating efficiency and highly accurate results when a few modes are used.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.509-514
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• 2001

It is well known that many real systems have asymmetric mass, damping and stiffness matrices. In this case, the method for calculating eigenpair sensitivity is different from that of symmetric system. To determine the derivatives of the eigenpairs in asymmetric damped case, a modal method was recently developed by Adhikari. When a dynamic system has many degrees of freedom only a few lower modes are available, and because the higher modes should be truncated to use the modal method, the errors may become significant. In this paper a procedure for determining the sensitivities of the eigenpairs of asymmetric damped system using a few lowest set of modes is proposed. Numerical examples show that proposed method achieves better calculating efficiency and highly accurate results when a few modes are used.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.530-533
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• 2004

It is well known that many real systems have asymmetric mass, damping and stiffness matrices. In this case, the method for calculating eigenpair sensitivity is different from that of symmetric system. To determine the derivatives of the eigenpairs in asymmetric damped case, a modal method was recently developed by Adhikari. When a dynamic system has many degrees of freedom, only a few lower modes are available, and because the higher modes should be truncated to use the modal method, the errors may become significant. In this paper a procedure for determining the sensitivities of the eigenpairs of asymmetric damped system using a few lowest set of modes is proposed. Numerical examples show that proposed method achieves better calculating efficiency and highly accurate results when a few modes are used.

• Structural Engineering and Mechanics
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• 제29권3호
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• pp.241-258
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• 2008

This paper presents a new identification approach to prestress force. Firstly, a bridge deck is modeled as a prestressed Timoshenko beam. The time domain responses of the beam under sinusoidal excitation are studied based on modal superposition. The prestress force is then identified in the time domain by a system identification approach incorporating with the regularization of the solution. The orthogonal polynomial function is used to improve the noise effect and obtain the derivatives of modal responses of the bridge. Good identification results are obtained from only the first few measured modal data under both sinusoidal and impulsive excitations. It is shown that the proposed method is insensitive to the magnitude of force to be identified and can be successfully applied to indirectly identify the prestress force as well as other physical parameters, such as the flexural rigidity and shearing rigidity of a beam even under noisy environment.

• Structural Engineering and Mechanics
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• 제77권4호
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• pp.495-508
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• 2021

This study devises a novel approach, namely quadruple 1D convolutional neural network, for detecting connection stiffness reduction in steel truss bridge structure using experimental and numerical modal data. The method is developed based on expertise in two domains: firstly, in Structural Health Monitoring, the mode shapes and its high-order derivatives, including second, third, and fourth derivatives, are accurate indicators in assessing damages. Secondly, in the Machine Learning literature, the deep convolutional neural networks are able to extract relevant features from input data, then perform classification tasks with high accuracy and reduced time complexity. The efficacy and effectiveness of the present method are supported through an extensive case study with the railway Nam O bridge. It delivers highly accurate results in assessing damage localization and damage severity for single as well as multiple damage scenarios. In addition, the robustness of this method is tested with the presence of white noise reflecting unavoidable uncertainties in signal processing and modeling in reality. The proposed approach is able to provide stable results with data corrupted by noise up to 10%.

• Wind and Structures
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• 제14권5호
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• pp.413-434
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• 2011

Without output covariance estimation, one reference-based Stochastic Subspace Technique (SST) for extracting modal parameters and flutter derivatives of bridge deck is developed and programmed. Compared with the covariance-driven SST and the oscillation signals incurred by oncoming or signature turbulence that adopted by previous investigators, the newly-presented identification scheme is less time-consuming in computation and a more desired accuracy should be contributed to high-quality free oscillated signals excited by specific initial displacement. The reliability and identification precision of this technique are confirmed by a numerical example. For the 3-DOF sectional models of Sutong Bridge deck (streamlined) and Suramadu Bridge deck (bluff) in wind tunnel tests, with different wind velocities, the lateral bending, vertical bending, torsional frequencies and damping ratios as well as 18 flutter derivatives are extracted by using SST. The flutter derivatives of two kinds of typical decks are compared with the pseudo-steady theoretical values, and the performance of $H_1{^*}$, $H_3{^*}$, $A_1{^*}$, $A_3{^*}$ is very stable and well-matched with each other, respectively. The lateral direct flutter derivatives $P_5{^*}$, $P_6{^*}$ are comparatively more accurate than other relevant lateral components. Experimental procedure seems to be more critical than identification technique for refining the estimation precision.

• Wind and Structures
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• 제10권3호
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• pp.215-232
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• 2007

This paper presents an aeroelastic analysis procedure to highlight the influence of wind velocity on the structural damping and frequency of a long span cable-stayed bridge. Frequency dependent self-excited forces in terms of flutter derivatives are expressed as continuous functions using rational function approximation technique. The aeroelastically modified structural equation of motion is expressed in terms of frequency independent modal state-space parameters. The modal logarithmic dampings and frequencies corresponding to a particular wind speed are then determined from the eigen solution of the state matrix.