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The purpose of this paper is to propose one analytical method to make stochastic floor response spectra in order to easily estimate the dynamic characteristics of secondary system such as piping, equipment and so on, under the stochastic non-stationary excitation and model uncertainty. Applying the transition matrix method with state space to the secondary system mounted on main structure, the non-stationary standard deviation of absolute acceleration response relating to the secondary system is obtained under the assumption of no structural uncertain properties. Then, finally, in order to obtain the statistical results of response in consideration of model uncertainty, through combining the extreme value theory, FOSM(First Order Second Moment) method and ACO(Ant Colony Optimization) algorithm, the floor response spectra can be stochastically derived. This proposed floor response spectra may be called the Stochastic Floor Response Spectra. The analytical results are compared with those by Monte Carlo simulation, and show the accuracy and efficiency.

A stochastic response spectrum method is proposed for simple evaluation of the structural response of an actively controlled aseismic structure. The response spectrum is constructed assuming a linear structure with an active mass damper (AMD) system, and an earthquake wave model given by the product of a non-stationary envelope function and a stationary Gaussian random process with Kanai-Tajimi power spectral density. The control design is executed using a linear quadratic Gaussian control strategy for an enlarged state space system, and the response amplification factor is given by the combination of the obtained statistical response values and extreme value theory. The response spectrum thus produced can be used for simple dynamical analyses. The response factors obtained by this method for a multi-degree-of-freedom structure are shown to be comparable with those determined by numerical simulations, demonstrating the validity and utility of the proposed technique as a simple design tool. This method is expected to be useful for engineers in the initial design stage for structures with active aseismic control.

The regulatory guide for seismic design of nuclear power plant has been vastly revised at several fields. Main items under revision are observed such as the requirement of making appropriate concern for the dynamic coupling effects of horizontal and vertical components of earthquake, and the consideration of probabilistic risk assessment against the uncertainty of earthquake. The purpose of this paper, therefore, is to estimate the stochastic responses of multi-degree-of-freedom structure with closely spaced natural frequencies under the consideration of the correlations between multi components of earthquake. For this target, one mathematical model is developed in order to analytically evaluate the effects of correlation between components of input, and the stochastic vibration analysis is executed based on FEM-based eigen mode analysis and transition matrix method. The analytical results are compared with those by Monte Carlo simulation. Failure probability of structure is also explained as a typical example applying the proposed technique to the probabilistic seismic design.

The building structure is modeled as a linear single-degree-of-freedom system, and an active mass damper (AMD) is also adopted as the control device in order to reduce the structural response due to the external random load. In addition, suppose that the input acceleration of earthquake can be modeled as the product of nonstationary envelope function and narrow-band stationary random process with Kanai-Tajimi spectrum. In order to obtain the nonstationary stochastic response of control system due to the narrow-band nonstationary random process, in consideration of exchanging the active control mode for the passive one, considerable efforts are generally required in the analytical formulation. This paper, therefore, proposes an analytical technique to acquire the response covariance matrix by utilizing the state transition matrix method in state space. The proposed technique is evaluated by comparing the analytical results with those from numerical simulations.

This paper outlines shaking table tests and their results for an active seismic response control system that uses fuzzy optimal logic (FOL). The test results confirmed the validity of the vibration control effect of this seismic response control system. The results of this study lead to two conclusions, that the effectiveness of this FOL control system can be increased by modifying the membership function, and that the results of seismic response control tests can be qualitatively evaluated by simple simulation methods.

A method to estimate the stochastic response of hysteretic structures under combined random loads regarded as Gaussian white noise is investigated. The response statistical moments of structures, with hysteretic characteristics approximated by Wen's mathematical model, are obtained by using the Fokker-Planck equation method with a cumulant truncation technique. This paper deals with the formulation for the multi-degree-of-freedom system, and demonstrates that resulting variances of the response for a three-degree-of-freedom structure, as a numerical example, agree well with a Monte Carlo simulation.

The study of safety factor estimation in seismic probabilistic safety assessment has been a focus of researchers' interest for some time. Most of the papers dealt with the safety factor estimation by means of experimental knowledge or numerical analysis such as the Monte Carlo technique. This paper presents a new method to gain parts of structural response factors analytically by utilizing the statistical theory of extremes and the stochastic FEM technique. First, the stochastic FEM is adopted to obtain the statistical response values considering the uncertainty of structural material, through the spectral analysis due to an earthquake as a stationary random process. As second step, combining the results by statistical theory of extremes for a structure having deterministic material properties with the previous results by spectral analysis considering material uncertainty, with the aid of the total representation theorem against uncertainty modeling, statistics related to maximum values of response could be calculated under the consideration of structural material uncertainty. Those results are shown in good agreement with Monte Carlo simulation. Finally, using the obtained results, it is shown how to get the structural safety factors related to structural material uncertainty analytically.

Recent research related to probability-based structural design has become more active, especially in the field of the load and resistance factor design (LRFD) technique. This paper also describes some contributions to the improvement of the LRFD method. In this paper, a rational and analytical method to determine the required code format and load factors, which were determined experimentally in many former LRFD studies, considering the dynamic characteristics of a structure is newly proposed on the basis of the dynamic reliability technique with the load combination theory. The usefulness of this proposed method is described in an application to the selection problem of the required code format and load factors against a typical structure that is flexible and excited due to multiple random loads.

The purpose of this paper is to propose a newly floor response spectra (FRS) in order to evaluate simply the structural response of the actively-controlled secondary system subjected to earthquake. This paper adopts a linear single-degree-of-freedom system as a main structure and an active mass damper (AMD) system as the active control technology. Also, the earthquake wave is modeled as product of a non-stationary envelope function and a stationary Gaussian random process of which power spectral density is equal to the Kanai-Tajimi spectrum. The control design is executed by using linear quadratic Gaussian control strategy against an enlarged state space system. Finally, the response amplification factor is given by the combination of the obtained statistical response values and the extreme value theory. Analytical results are compared with numerical simulations, and both show a good agreement. As a result, it seems that the validity of the proposed technique is confirmed.Copyright © 2011 by ASME

The purpose of this paper is to estimate the real time vibration control of an actively-controlled nonlinear structure due to non-stationary external loads. When the optimal control theory is adopted as a control law against the concerned task, the derivation of time dependent optimal control gains may be required because of a remarkable non-stationarity of response amplitude. In addition, since the system is nonlinear, it takes more time to calculate those time dependent gains. This means that it is difficult to strictly execute the real time active control with optimal control theory as for the non-stationary and nonlinear system. In this paper, therefore, one approximate technique, coupled fuzzy-optimal control, is proposed in order to realize the real time control of non-stationary and nonlinear system. Finally, results by deterministic analysis based on numerical simulations are compared with those by stochastic analysis using statistical equivalent linearization technique.Copyright © 2010 by ASME

The authors have attempted to develop an analytical method that estimates the variability of structural response by treating the variations in the physical properties of structures by means of the stochastic finite-element method and by treating the random variation in earthquake excitations by means of the random vibration theory, and to further encode the method of analysis. This article describes the formulation of variability of response used in the analytical method, and then shows the results of benchmark analysis with the Monte Carlo method to confirm the accuracy of the analytical method. The floor response spectrum of a reactor building was also analyzed as an example in order to demonstrate the validity of this method.

A finite element formulation for a class of nonlinear viscoelastic continua subjected to stochastic excitation is developed by means of a stochastic equivalent linearization technique. The nonlinear viscoelastic properties of the continua are modeled in terms of the constitutive equation which linearly involves the hysteretic tensor and in terms of the auxiliary equation which describes a nonlinear relationship among the strain and hysteretic tensors and their time derivatives. This auxiliary equation is linearized with the aid of a stochastic linearization technique which minimizes the expected value of the square of the difference between the nonlinear and linearized auxiliary equations. The linearized boundary value problem then involves a set of two linearization coefficients which are functions of space and time. With the aid of the weighted residuals method, the boundary value problem developed for the continuum is transformed into that in the finite element formulation. In integrating the equation ...

This paper presents a new method to gain the structural reliability of a nonlinear single degree of freedom system with the material uncertainty and deteriorating characteristics due to a nonzero mean random excitation, by utilizing the Fokker-Planck equation approach (F-P method). Since the obtained moment equations of nonlinear systems by F-P method are not closed form, some approximations should be taken to get the closed form. In the presented paper, the response moments can be obtained to analyze the closed moment equations which are derived from the approximation of higher-order moments by lower-order moments with the aid of a truncation technique of higher-order cumulants. This paper shows the analysis of a Duffing oscillator subjected to a stationary Gaussian white noise as a typical example, and demonstrates that the resulting statistical values of the response agree well with the Monte Carlo simulation.