• Smart Structures and Systems
• /
• 제19권1호
• /
• pp.21-31
• /
• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Earthquakes and Structures
• /
• 제10권5호
• /
• pp.1233-1251
• /
• 2016

In this paper, it is aimed to determine the stochastic response of a suspension bridge subjected to spatially varying ground motions considering the geometric nonlinearity. Bosphorus Suspension Bridge built in Turkey and connects Europe to Asia in Istanbul is selected as a numerical example. The spatial variability of the ground motion is considered with the incoherence, wave-passage and site-response effects. The importance of site-response effect which arises from the difference in the local soil conditions at different support points of the structure is also investigated. At the end of the study, mean of the maximum and variance response values obtained from the spatially varying ground motions are compared with those of the specialised cases of the ground motion model. It is seen that each component of the spatially varying ground motion model has important effects on the dynamic behaviour of the bridge. The response values obtained from the general excitation case, which also includes the site-response effect causes larger response values than those of the homogeneous soil condition cases. The variance values calculated for the general excitation case are dominated by dynamic component at the deck and Asian side tower. The response values obtained for the site-response effect alone are larger than the response values obtained for the incoherence and wave-passage effects, separately. It can be concluded that suspension bridges are sensitive to the spatial variability of ground motion. Therefore, the incoherence, the wave-passage and especially the site-response effects should be considered in the stochastic analysis of this type of engineering structures.

• Steel and Composite Structures
• /
• 제22권5호
• /
• pp.1001-1018
• /
• 2016

The purpose of this paper is to compare the structural responses obtained from the stochastic analysis of a suspension bridge subjected to uniform and partially correlated seismic ground motions, using different spatial correlation functions commonly used in the earthquake engineering. The spatial correlation function employed in this study consists of a term that characterizes the loss of coherency. To account for the spatial variability of ground motions, the widely used four loss of coherency models in the literature has been taken into account in this study. Because each of these models has its own characteristics, it is intended to determine the sensitivity of a suspension bridge due to these losses of coherency models which represent the spatial variability of ground motions. Bosporus Suspension Bridge connects Europe to Asia in Istanbul is selected as a numerical example. The bridge has steel towers that are flexible, inclined hangers and a steel box-deck of 1074 m main span, with side spans of 231 and 255 m on the European and Asian sides, respectively. For the ground motion the filtered white noise model is considered and applied in the vertical direction, the intensity parameter of this model is obtained by using the S16E component of Pacoima Dam record of 1971 San Fernando earthquake. An analytically simple model called as filtered white noise ground motion model is chosen to represent the earthquake ground motion. When compared with the uniform ground motion case, the results obtained from the spatial variability models with partial correlation outline the necessity to include the spatial variability of ground motions in the stochastic dynamic analysis of suspension bridges. It is observed that while the largest response values are obtained for the model proposed by Harichandran and Vanmarcke, the model proposed by Uscinski produces the smallest responses among the considered partially correlated ground motion models. The response values obtained from the uniform ground motion case are usually smaller than those of the responses obtained from the partially correlated ground motion cases. While the response values at the flexible parts of the bridge are totally dominated by the dynamic component, the pseudo-static component also has significant contributions for the response values at the rigid parts of the bridge. The results also show the consistency of the spatial variability models, which have different characteristics, considered in this study.

• 한국멀티미디어학회논문지
• /
• 제9권11호
• /
• pp.1503-1514
• /
• 2006

오늘날 대부분의 고객들이 어디에서든지 인터넷을 사용할 수 있게 됨에 따라, 대부분의 기업들이 자신들의 서비스를 인터넷상에서 제출하게 되었다. 그 결과 무수히 많은 웹 서비스 시스템이 이미 인터넷상에서 서비스를 하고 있으며 더 많은 시스템들이 구축 중이다. 그래서 구축 중인 시스템이 교착상태와 같은 문제점이 없이 성공적으로 실행될 것이라는 것을 설계 초기 단계에 검증하는 방법에 대한 연구가 많이 수행되어 왔다. 페트리 넷을 이용하는 방법들도 몇 가지 소개되었는데, 이들은 웹 서비스 시스템을 페트리 넷으로 표현하는 방법에 주안점을 두고 있으며, 효율적인 분석 방법에 대한 연구는 부족한 실정이다. '최소 순회 시간' 방법은 '시간 넷'(Timed Net)에서 모든 트랜지션(transition)들을 최소한 한번 이상 격발하고 초기 마킹으로 되돌아오는데 걸리는 최소 시간을 찾아주는 수학적 방법으로, 컴퓨터 시스템 분석에 널리 사용된다. 시간 넷은 트랜지션에 지연 시간이 연합된 변형된 페트리 넷으로. 실세계에서의 지연시간은 확률적임에도 불구하고 기존의 시간 넷에서는 상수가 사용된다. 본 논문은 사건의 실행 시간이 화률 분포를 이루는 '혼합 분포 확률 시간 넷'을 제안하고 '혼합 분포 확률 시간 넷'의 최소 순회 시간 분석 방법을 소개한다. 또한 '혼합 분포 확률 시간 넷'의 최소순회시간 분석을 이용하여 웹 서비스 시스템의 응답 시간을 분석하는 방법을 보인다.

• Structural Engineering and Mechanics
• /
• 제28권2호
• /
• pp.129-152
• /
• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Structural Engineering and Mechanics
• /
• 제38권1호
• /
• pp.39-63
• /
• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• 한국안전학회지
• /
• 제25권3호
• /
• pp.91-99
• /
• 2010

In this study, the advanced numerical algorithm is developed which can performed the static and dynamic stochastic finite element analysis by considering the effect of uncertainties included in the member stiffness of steel cable-stayed bridges and seismic load. After conducting the linear and nonlinear initial shape analysis, the advanced numerical algorithm is the assessment tool which can performed structural the response analysis considering the static linearity and non-linearity of before or after induced intial tensile force, and examined the reliability assessment more efficiently. The verification of the developed numerical algorithm is evaluated by analyzing the regression analysis and coefficient of correlation using the direct monte carlo simulation. Also, the dynamic response characteristic and coefficient of variation of the steel cable-stayed bridge is calculated by considering the uncertainty of random variables using the developed numerical algorithm. In addition, the quantitative structural safety of the steel cable-stayed bridges is evaluated by conducting the reliability assessment based upon the dynamic stochastic finite element analysis result.

• Earthquakes and Structures
• /
• 제10권6호
• /
• pp.1451-1465
• /
• 2016

The effectiveness of base isolation (BI) systems for mitigation of seismic vibration of bridges have been extensively studied in the past. It is well established in those studies that the performance of BI system is largely dependent on the characteristics of isolator yield strength. For optimum design of such systems, normally a standard nonlinear optimization problem is formulated to minimize the maximum response of the structure, referred as Stochastic Structural Optimization (SSO). The SSO of BI system is usually performed with reference to a problem of unconstrained optimization without imposing any restriction on the maximum isolator displacement. In this regard it is important to note that the isolator displacement should not be arbitrarily large to fulfil the serviceability requirements and to avoid the possibility of pounding to the adjacent units. The present study is intended to incorporate the effect of excessive isolator displacement in optimizing BI system to control seismic vibration effect of bridges. In doing so, the necessary stochastic response of the isolated bridge needs to be optimized is obtained in the framework of statistical linearization of the related nonlinear random vibration problem. A simply supported bridge is taken up to elucidate the effect of constraint condition on optimum design and overall performance of the isolated bridge compared to that of obtained by the conventional unconstrained optimization approach.

• 한국전산구조공학회논문집
• /
• 제20권6호
• /
• pp.789-799
• /
• 2007

본 논문에서는 구조의 재료물성치와 기하학적 인수의 공간적 불확실성에 의한 구조 응답변화도 산정을 위한 정식화를 제안하였다. 정식화는 추계론적 유한요소해석의 해석법 중의 하나인 가중적분법을 기본으로 하였다. 해석 대상 구조는 전단변형을 포함하는 평판구조로서, 평판구조에 나타날 수 있는 불확실 인수로는 재료적 측면에서는 재료탄성계수와 포아송비가 있으며, 기하학적 인수로는 평판의 두께를 들 수 있다. 선형탄성 영역에서 선형성을 나타내는 재료탄성계수와는 달리 평판의 두께는 3차함수로 강성에 기여하고, 포아송비의 경우 분수의 형태로 강성에 기여하므로 직접적으로는 이를 추계론적 해석에 고려할 수 없다. 따라서 본 연구에서는 적합행렬내의 포아송비를 Taylor전개하여 사용하였다. 제안된 정식화에 의한 결과는 기존 연구결과는 물론 몬테카를로 해석에 의한 결과와도 비교하여 제안한 정식화를 검증하였다.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 춘계학술대회논문집
• /
• pp.414-419
• /
• 2001

In this research, reliability based optimum design is presented for the thin walled beam structures. Deterministic and stochastic optimum design are compared for the thin walled beam structures. Monte Carlo simulation is used for stochastic optimum design with consideration of probabilistic distribution of representative section properties of the thin walled beams with the Response Surface Method.