• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06a
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• pp.686-691
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• 1994

For evaluating the response fluctuation of the actual environmental acoustic system excited by arbitrary random inputs, it is important to predict a whole probability distribution form closely connected with evaluation indexes Lx, Leq and so on. In this paper, a new type evaluation method is proposed by introducing three functional models matched to the prediction of the response probability distribution from a problem-oriented viewpoint. Because of the positive variable of the sound intensity, the response probability density function can be reasonably expressed theoretically by a statistical Laguerre expansion series form. The relationship between input and output is described by the regression relationship between the distribution parameters(containing expansion coefficients of this expression) and the stochastic input. These regression functions are expressed in terms of the orthogonal series expansion and their parameters are determined based on the least-squares error criterion and the measure of statistical independency.

• Structural Engineering and Mechanics
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• v.3 no.3
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• pp.273-287
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• 1995

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.959-982
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• 2015

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

• Wind and Structures
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• v.10 no.1
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• pp.45-60
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• 2007

Transmission tower is a vital component in electrical system. In order to accurately compute the dynamic response and reliability of transmission tower under the excitation of wind loading, a new method termed as probability density evolution method (PDEM) is introduced in the paper. The PDEM had been proved to be of high accuracy and efficiency in most kinds of stochastic structural analysis. Consequently, it is very hopeful for the above needs to apply the PDEM in dynamic response of wind-excited transmission towers. Meanwhile, this paper explores the wind stochastic field from stochastic Fourier spectrum. Based on this new viewpoint, the basic random parameters of the wind stochastic field, the roughness length $z_0$ and the mean wind velocity at 10 m heigh $U_{10}$, as well as their probability density functions, are investigated. A latticed steel transmission tower subject to wind loading is studied in detail. It is shown that not only the statistic quantities of the dynamic response, but also the instantaneous PDF of the response and the time varying reliability can be worked out by the proposed method. The results demonstrate that the PDEM is feasible and efficient in the dynamic response and reliability analysis of wind-excited transmission towers.

• Structural Engineering and Mechanics
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• v.15 no.4
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• pp.381-394
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• 2003

While constructing multistorey buildings with reinforced concrete framed structures it is a common practice to provide parking space for vehicles at the ground floor level. This floor will generally consist of open frames without any infilled walls and is called an open-storey. From a post disaster damage survey carried out, it was noticed that during the January 26, 2001 Bhuj (Gujarat, India) earthquake, a large number of reinforced concrete framed buildings with open-storey at ground floor level, suffered extensive damage and in some cases catastrophic collapse. This has brought into sharp focus the need to carry out systematic studies on the seismic vulnerability of such buildings. Determination of vulnerability requires realistic structural response estimations taking into account the stochasticity in the loading and the system parameters. The stochastic finite element method can be effectively used to model the random fields while carrying out such studies. This paper presents the details of stochastic finite element analysis of a five-storey three-bay reinforced concrete framed structure with open-storey subjected to standard seismic excitation. In the present study, only the stochasticity in the system parameters is considered. The stochastic finite element method used for carrying out the analysis is based on perturbation technique. Each random field representing the stochastic geometry/material property is discretised into correlated random variables using spatial averaging technique. The uncertainties in geometry and material properties are modelled using the first two moments of the corresponding parameters. In evaluating the stochastic response, the cross-sectional area and Young' modulus are considered as independent random fields. To study the influence of correlation length of random fields, different correlation lengths are considered for random field discretisation. The spatial expectations and covariances for displacement response at any time instant are obtained as the output. The effect of open-storey is modelled by suitably considering the stiffness of infilled walls in the upper storey using cross bracing. In order to account for changes in soil conditions during strong motion earthquakes, both fixed and hinged supports are considered. The results of the stochastic finite element based seismic analysis of reinforced concrete framed structures reported in this paper demonstrate the importance of considering the effect of open-storey with appropriate support conditions to estimate the realistic response of buildings subjected to earthquakes.

• Steel and Composite Structures
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• v.15 no.1
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• pp.15-39
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• 2013

The sensitivities of a structural response due to variation of its design parameters are prerequisite in the majority of the algorithms used for fundamental problems in engineering as system uncertainties, identification and probabilistic assessments etc. The paper presents the concept of probabilistic sensitivity of suspension bridges with respect to near-fault ground motion. In near field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many suspension bridges have significant structural response modes. Two different types of suspension bridges, which are Bosporus and Humber bridges, are selected to investigate the near-fault ground motion effects on suspension bridges random response sensitivity analysis. The modulus of elasticity is selected as random design variable. Strong ground motion records of Kocaeli, Northridge and Erzincan earthquakes are selected for the analyses. The stochastic sensitivity displacements and internal forces are determined by using the stochastic sensitivity finite element method and Monte Carlo simulation method. The stochastic sensitivity displacements and responses obtained from the two different suspension bridges subjected to these near-fault strong-ground motions are compared with each other. It is seen from the results that near-fault ground motions have different impacts stochastic sensitivity responses of suspension bridges. The stochastic sensitivity information provides a deeper insight into the structural design and it can be used as a basis for decision-making.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.19-37
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• 2013

The optimum design of base isolation system considering model parameter uncertainty is usually performed by using the unconditional response of structure obtained by the total probability theory, as the performance index. Though, the probabilistic approach is powerful, it cannot be applied when the maximum possible ranges of variations are known and can be only modelled as uncertain but bounded type. In such cases, the interval analysis method is a viable alternative. The present study focuses on the bounded optimization of base isolation system to mitigate the seismic vibration effect of structures characterized by bounded type system parameters. With this intention in view, the conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems correspond to a lower bound and upper bound optimum solutions. A lead rubber bearing isolating a multi-storeyed building frame is considered for numerical study to elucidate the proposed bounded optimization procedure and the optimum performance of the isolation system.

• Proceedings of the Korea Society for Simulation Conference
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• 1994.10a
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• pp.1-2
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• 1994

With the prevalence of computers in modern organizations, simulation is receiving more atention as an effectvie decision -making tool. Simualtion is a computer-based numerical technique which uses mathmatical and logical models to approximate the behaviror of a real-world system. However, iptimization of synamic stochastic systems often defy analytical and algorithmic soluions. Although a simulation approach is often free fo the liminting assumption s of mathematical modeling, cost and time consiceration s make simulation the henayst's last resort. Therefore, whenever possible, analytical and algorithmica solutions are favored over simulation. This paper discussed the issues and procedrues for using simulation as a tool for optimization of stochastic complex systems that are dmodeled by computer simulation . Its emphasis is mostly on issues that are speicific to simulation optimization instead of consentrating on the general optimizationand mathematical programming techniques . A simulation optimization problem is an optimization problem where the objective function. constraints, or both are response that can only be evauated by computer simulation. As such, these functions are only implicit functions of decision parameters of the system, and often stochastic in nature as well. Most of optimization techniqes can be classified as single or multiple-resoneses techniques . The optimization of single response functins has been researched extensively and consists of many techniques. In the single response category, these strategies are gradient based search techniques, stochastic approximate techniques, response surface techniques, and heuristic search techniques. In the multiple response categroy, there are basically five distinct strategies for treating the responses and finding the optimum solution. These strategies are graphica techniqes, direct search techniques, constrained optimization techniques, unconstrained optimization techniques, and goal programming techniques. The choice of theprocedreu to employ in simulation optimization depends on the analyst and the problem to be solved. For many practival and industrial optimization problems where some or all of the system components are stochastic, the objective functions cannot be represented analytically. Therefore, modeling by computersimulation is one of the most effective means of studying such complex systems. In this paper, after discussion of simulation optmization techniques, the applications of above techniques will be presented in the modeling process of many flexible manufacturing systems.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.451-455
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• 1993

Interaction between system and disturbance results in system with time-dependent parameter. Parameter variation due to interaction has random characteristics. Most of the randomly varying parameters in control problem is regarded as white noise random process which is not a realistic model. In real situation those random variation is colored noise random process. Modified F-P-K equation is proposed to get the response of the random parametric system using some correction factor. Proposed technique is employed to obtain the colored noise parametric system response and confirmed via Monte-Carlo Simulation.