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

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.

Modified Probability Density Evolution Method for the Solution of Multi-Degree-of-Freedom Nonlinear Stochastic Dynamical Systems

2017 ◽  
Author(s):  
Xiaoyu Zhou ◽  
Hongxia Li ◽  
Yi Huang
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
High Efficiency ◽  
Polynomial Regression ◽  
Degree Of Freedom ◽  
Engineering Practice ◽  
Density Evolution ◽  
Stochastic Dynamical Systems ◽  
Epr Method ◽  
Probability Density Evolution

A probability density evolution based exponential polynomial regression (PDEM-EPR) method to calculate the probability density function (PDF) of the high dimensional nonlinear stochastic dynamical systems is presented in this paper. Several typical examples, such as linear oscillator and Duffing oscillator are solved by PDEM-EPR method, and the results fit well with the analytical solutions. An engineering practice problem of ship nonlinear random roll in the beam waves is involved in this paper. The results obtained by PDEM-EPR is compared with those obtained by path integral method. The later results were given by Chai Wei [3]. It shows that PDEM-EPR method has the advantages as following: 1) The multi-degree-of-freedom (MDOF) nonlinear stochastic dynamical problems can be solved by PDEM-EPR method; 2) High efficiency can be obtained by PDEM-EPR method.

scholarly journals Random Vibration Analysis of Train Moving over Slab Track on Bridge under Track Irregularities and Earthquakes by Pseudoexcitation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Zhiping Zeng ◽  
Kunteng Zhu ◽  
Xianfeng He ◽  
Wentao Xu ◽  
Lingkun Chen ◽  
...  
Keyword(s):  
High Speed ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Element Model ◽  
Earthquake Intensity ◽  
Dynamic Reliability ◽  
Slab Track ◽  
First Passage Failure ◽  
Operation Stability ◽  
Track Irregularities

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.

A Nonlinear Vehicle-Road Coupled Model for Dynamics Research

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Shaohua Li ◽  
Shaopu Yang ◽  
Liqun Chen
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Equations Of Motion ◽  
Coupled Model ◽  
Coupled System ◽  
Computational Accuracy ◽  
Road Pavement ◽  
Nonlinear Viscoelastic ◽  
Road Surface Roughness ◽  
Leaderman Constitutive Relation

This paper presents a nonlinear vehicle-road coupled model which is composed of a seven-degree of freedom (DOF) vehicle and a simply supported double-layer rectangular thin plate on a nonlinear viscoelastic foundation. The nonlinearity of suspension stiffness, suspension damping and tire stiffness is considered and the Leaderman constitutive relation and Burgers model are applied to describe the nonlinear and viscoelastic properties of the asphalt topping material. The equations of motion for the vehicle-road system are derived and the partial differential equation of road pavement is discretized into an infinite number of second-order ordinary differential equations and first-order ordinary differential equations by Galerkin’s method and a mathematic transform. A numerical integration method for solving this coupled system is developed and the nonlinear dynamic behaviors of the system are analyzed. In addition, the simulation results of the coupled model are compared to those of the uncoupled traditional model. It is found that with the increase of harmonic road surface roughness amplitude, the vehicle body’s vertical response is always periodic, whereas the pavement’s response varies from quasi-periodic motion to chaotic motion. In the case of a heavy-duty vehicle, a soft subgrade or a higher running speed, the application of the proposed nonlinear vehicle-road coupled model would bring higher computational accuracy and make it possible to design the vehicle and pavement simultaneously.

Coherent phenomena in stochastic dynamical systems

1999 ◽  
Vol 169 (2) ◽  
pp. 171 ◽  
Author(s):  
Valerii I. Klyatskin ◽  
D. Gurarie
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

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