Random Vibration and Dynamic Reliability Analyses for Nonlinear MDOF Systems under Additive Excitations via DPIM

This paper investigates the random vibration and the dynamic reliability of operation stability of train moving over slab track on bridge under track irregularities and earthquakes by the pseudoexcitation method (PEM). Each vehicle is modeled by multibody dynamics. The track and bridge is simulated by a rail-slab-girder-pier interaction finite element model. The coupling equations of motion are established based on the wheel-rail interaction relationship. The random excitations of the track irregularities and seismic accelerations are transformed into a series of deterministic pseudoexcitations by PEM. The time-dependent power spectral densities (PSDs) of the random vibration of the system are obtained by step-by-step integration method, and the corresponding dynamic reliability is estimated based on the first-passage failure criterion. A case study is then presented in which a high-speed train moves over a slab track resting on a simply supported girder bridge. The PSD characteristics of the random vibration of the bridge and train are analyzed, the influence of the wheel-rail-bridge interaction models on the random vibration of the bridge and train is discussed, and furthermore the influence of train speed, earthquake intensity, and pier height on the dynamic reliability of train operation stability is studied.

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Application of Auto-Covariance Orthogonal Decomposition in the Response of Multi Degree of Freedom (MDOF) Systems to Non-Stationary Random Vibration Processes

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th AIAA/ASME/AHS Adaptive Structures Conference<BR> 12th ◽

10.2514/6.2010-3014 ◽

2010 ◽

Cited By ~ 2

Author(s):

Karen Scott ◽

Sameer Mulani ◽

Rakesh Kapania

Keyword(s):

Random Vibration ◽

Orthogonal Decomposition ◽

Degree Of Freedom ◽

Mdof Systems ◽

Auto Covariance

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Approximate Nonstationary Random Vibration Analysis for MDOF Systems

Journal of Applied Mechanics ◽

10.1115/1.3173629 ◽

1988 ◽

Vol 55 (1) ◽

pp. 197-200 ◽

Cited By ~ 13

Author(s):

C. G. Bucher

Keyword(s):

Exact Solutions ◽

Approximate Method ◽

Vibration Analysis ◽

Random Vibration ◽

Computer Time ◽

Additional Benefit ◽

Mdof Systems ◽

Order Of Magnitude ◽

Random Vibration Analysis ◽

Good Agreement

An approximate method for nonstationary random vibration analysis is presented. This method utilizes properties of the stationary solution for simplifying the analysis. This approach has previously been applied by the author to linear and nonlinearly damped SDOF systems. In the present paper the concept is extended to linear MDOF systems and applied to nonstationary earthquake-type loading. Comparisons with available exact solutions show very good agreement in numerical results with the additional benefit of reducing computer time by more than one order of magnitude.

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Seismic Reliability Analysis of MDOF Systems Based on Odd Exponent Wavelet

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.194-196.1711 ◽

2011 ◽

Vol 194-196 ◽

pp. 1711-1715

Author(s):

Mei Ling Xiao ◽

Liao Yuan Ye ◽

Chun Tao Gao

Keyword(s):

Reliability Analysis ◽

Structural Response ◽

Maximum Probability ◽

Structural Dynamic ◽

Seismic Reliability ◽

Dynamic Reliability ◽

Mdof Systems ◽

First Passage Failure ◽

Duhamel Integral ◽

Primary Advantage

This study proposed non-failure or non-disabled probability of structure suffering random dynamic load within given time. A wavelet method based on its conception was proposed for seismic dynamic reliability analysis of MDOF system：From the Duhamel integral of the dynamic structural response, the structure stochastic response was expressed as earthquake ground motion’s wavelet transform. The ground motion and structure responses were modeled as non-stationary random process using odd exponent wavelets. The first-passage failure criterion and maximum probability were employed to estimate the structural dynamic reliability. The primary advantage of the proposed method is that it does not need to calculate spectral moments from the power density function integral, which are usually difficult to obtain the analytical expressions.

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Seismic Reliability Analysis of Long-Span Cable-stayed Bridges

The Open Civil Engineering Journal ◽

10.2174/1874149501509010592 ◽

2015 ◽

Vol 9 (1) ◽

pp. 592-597

Author(s):

Wu Fangwen ◽

Yang Caofang ◽

Xue Chengfeng ◽

Ji Zhengdi

Keyword(s):

Reliability Analysis ◽

Cross Sections ◽

Random Vibration ◽

Earthquake Resistance ◽

Seismic Reliability ◽

Dynamic Reliability ◽

Vibration Theory ◽

First Passage Failure ◽

First Order Second Moment ◽

Cable Stayed Bridges

Earthquake motion is a random process, and thus, analyzing the seismic responses and dynamic reliability of cable-stayed bridges based on the random vibration theory is important. In this paper, dynamic reliability is investigated under earthquake loads by applying the stochastic vibration theory to the Sutong Yangtze River Highway Bridge. The response statistics are obtained from random vibration analyses, and the dynamic reliability of the normal stress of several key cross sections in the bridge is analyzed using the first-order second-moment method and the first-passage failure theory. The dynamic reliability analysis shows that the reliability index changes with girder section location and meets the design requirements. The analysis shows that the Sutong Bridge has adequate earthquake resistance ability. The structure’s earthquake resistance is appraised to provide an important theoretical reference for improving the seismic resistance design methods.

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Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus

Journal of Mathematics ◽

10.1155/2021/9218857 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Yang Yan ◽

Xiaohong Yu

Keyword(s):

Dynamical Systems ◽

Probability Density ◽

Random Vibration ◽

Equations Of Motion ◽

Coupled System ◽

Accurate Method ◽

Computational Accuracy ◽

Stochastic Dynamical Systems ◽

Dynamic Reliability ◽

Representative Points

With the increasing load and speed of trains, the problems caused by various random excitations (such as safety and passenger comfort) have become more prominent and thus arises the necessity to analyze stochastic dynamical systems, which is important in both academic and engineering circles. The existing analysis methods are inadequate in terms of computational accuracy, computational efficiency, and applicability in solving complex problems. For that, a new efficient and accurate method is used in this paper, suitable for linear and nonlinear random vibration analysis of large structures as well as static and dynamic reliability assessment. It is the direct probability integration method, which is extended and applied to the random vibration reliability analysis of dynamical systems. Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. The simulation results show the influence of the number of representative points on the smoothness of the image of the probability density function and the accuracy of the calculation results.

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