• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.31-40
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• 2022

In structural engineering, the material properties of the structures such as elastic modulus, shear modulus, density, and size may not be deterministic and may vary at different locations. The dynamic response analysis of such structures may need to consider these properties as stochastic. This paper introduces a stochastic finite element method (SFEM) approach to analyze moving loads problems. Firstly, Karhunen-Loéve expansion (KLE) is applied for expressing the stochastic field of material properties. Then the mathematical expression of the random field is substituted into the finite element model to formulate the corresponding random matrix. Finally, the statistical moment of the dynamic response is calculated by the point estimation method (PEM). The accuracy and efficiency of the dynamic response obtained from the KLE-PEM are demonstrated by the example of a moving load passing through a simply supported Euler-Bernoulli beam, in which the material properties (including elastic modulus and density) are considered as random fields. The results from the KLE-PEM are compared with those from the Monte Carlo simulation. The results demonstrate that the proposed method of KLE-PEM has high accuracy and efficiency. By using the proposed SFEM, the random vertical deflection of a high-speed railway (HSR) bridge is analyzed by considering the random fields of material properties under the moving load of a train.

• Computers and Concrete
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• v.3 no.1
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• pp.1-15
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• 2006

The seismic safety of reinforced concrete containment building can be evaluated by probabilistic analysis considering randomness of earthquake, which is more rational than deterministic analysis. In the safety assessment of earthquake-resistant structures by the deterministic theory, it is not easy to consider the effects of random variables but the reliability theory and random vibration theory are useful to assess the seismic safety with considering random effects. The reliability assessment of reinforced concrete containment building subjected to earthquake load includes the structural analysis considering random variables such as load, resistance and analysis method, the definition of limit states and the reliability analysis. The reliability analysis procedure requires much time and labor and also needs to get the high confidence in results. In this study, random vibration analysis of containment building is performed with random variables as earthquake load, concrete compressive strength, modal damping ratio. The seismic responses of critical elements of structure are approximated at the most probable failure point by the response surface method. The response surface method helps to figure out the quantitative characteristics of structural response variability. And the limit state is defined as the failure surface of concrete under multi-axial stress, finally the limit state probability of failure can be obtained simply by first-order second moment method. The reliability analysis for the multiaxial strength limit state and the uniaxial strength limit state is performed and the results are compared with each other. This study concludes that the multiaxial failure criterion is a likely limit state to predict concrete failure strength under combined state of stresses and the reliability analysis results are compatible with the fact that the maximum compressive strength of concrete under biaxial compression state increases.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.2
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• pp.141-147
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• 2000

The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

• Structural Engineering and Mechanics
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• v.31 no.6
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• pp.737-749
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• 2009

The problem of estimating the dynamic response of a distributed parameter system excited by a moving vehicle with random initial velocity and random vehicle body mass is investigated. By adopting the Galerkin's method and modal analysis, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained, and then the dynamic response of the coupled system can be calculated in deterministic sense. The statistical characteristics of the responses of the system are computed by using improved perturbation approach with respect to mean value. This method is simple and useful to gather the stochastic structural response due to the vehicle-passenger-bridge interaction. Furthermore, some of the statistical numerical results calculated from the perturbation technique are checked by Monte Carlo simulation.

• Journal of KSNVE
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• v.8 no.4
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• pp.715-722
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• 1998

An investigation into the stochastic bifurcation and response statistics of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to genrage a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinanary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

• Nuclear Engineering and Technology
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• v.29 no.6
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• pp.476-487
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• 1997

To resolve several arguments raised for the current analysis of a structure like top hat, which is composed of flange, cylinder and plate, the dynamic response analysis is performed for the full and half models. The dynamic characteristics are investigated for full and half models and the results are compared between them. The responses such as bolt reactions and stresses due to random loading are also obtained using the analysis capabilities between commercial programs which have the routine for the random vibration analysis. Several general purpose structural analysis programs are used to get the response due to the random loadings. Also the application of the random loading and the effect of correlations such as fully correlated, partially correlated and fully uncorrelated cases are studied and the general directions for the generation of design loads due to random loading are suggested.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05d
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• pp.223-228
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• 1996

To resolve several arguments raised for the current analysis of a structure like top hat, which is composed of flange, cylinder and plate, the dynamic response analysis is performed for the full and half models. The dynamic characteristics are investigated for full and half models and the results are compared between them. The responses such as bolt reactions and stresses due to random loading are also obtained using the analysis capabilities between commercial programs which have the routine for the random vibration analysis. Several general purpose structural analysis programs are used to get the response due to the random loadings. Also the application of the random loading and the effect of correlations are studied and the general directions for the generation of design load due to random loading are suggested.

• Earthquakes and Structures
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• v.8 no.5
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• pp.1055-1067
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• 2015

A theoretical procedure to estimate spectral displacement of a hysteretic oscillator with bilinear stiffness excited by band-limited excitation is presented. The stochastic method of ground-motion simulation is combined with the random vibration theory to compute linear and nonlinear structural response. The response is obtained by computing the root-mean-square oscillator response using dissipation energy balancing by integrating over all energy levels of system weighting with the stationary probability density of the energy. The results are presented in a convenient form, and the accuracy of the procedure is assessed by comparison with results obtained with the time-domain method using the recorded data. The model shows little or no bias at the structural period of engineering interest.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.1
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• pp.147-169
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• 2024

In pace with the development of network technology at lightning speed, social networks have been extensively applied in our lives. However, as social networks retain a large number of users' sensitive information, the openness of this information makes social networks vulnerable to attacks by malicious attackers. To preserve the link privacy of individuals in social networks, an uncertain graph method based on node random response is devised, which satisfies differential privacy while maintaining expected data utility. In this method, to achieve privacy preserving, the random response is applied on nodes to achieve edge modification on an original graph and node differential privacy is introduced to inject uncertainty on the edges. Simultaneously, to keep data utility, a divide and conquer strategy is adopted to decompose the original graph into many sub-graphs and each sub-graph is dealt with separately. In particular, only some larger sub-graphs selected by the exponent mechanism are modified, which further reduces the perturbation to the original graph. The presented method is proven to satisfy differential privacy. The performances of experiments demonstrate that this uncertain graph method can effectively provide a strict privacy guarantee and maintain data utility.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.125-135
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• 2004

Industrial structure systems may have nonlinearity, and are also sometimes exposed to the danger of random excitation. This paper proposes a method to analyze response and reliability design of a complex nonlinear structure system under random excitation. The nonlinear structure system which is subjected to random process is modeled by finite element method. The nonlinear equations are expanded sequentially using the perturbation theory. Then, the perturbed equations are solved in probabilistic methods. Several statistical properties of random process that are of interest in random vibration applications are reviewed in accordance with the nonlinear stochastic problem.