Carsten Proppe

Equivalent linearization and Monte Carlo simulation in stochastic dynamics

Equivalent linearization (EQL) and Monte Carlo Simulation (MCS) are the most important techniques in analyzing large nonlinear structural systems under random excitation. This paper reviews the development and the state-of-the-art of EQL and MCS in stochastic structural dynamics.

Cross-wind effects on road and rail vehicles

This paper presents a review of recent research that has been carried out on the cross-wind effects on road and rail vehicles. After a brief introduction to the issues involved, the risk analysis framework is set out. All risk analysis methods require some knowledge of cross-wind aerodynamic force and moment coefficients, and methods of obtaining these through full scale and wind tunnel testing and through Computational Fluid Dynamics methods are then described. The picture of the flow fields around vehicles that is suggested by these measurements and calculations is then presented, and the steady and the unsteady aerodynamic force characteristics described. The detailed methodology for using this information to predict accident risk is then set out, including details of the vehicle dynamics system models that can be used. Finally potential alleviation methods are described and suggestions made for further works.

Exact stationary probability density functions for non-linear systems under Poisson white noise excitation

Abstract The paper presents exact stationary probability density functions for systems under Poisson white noise excitation. Two different solution methods are outlined. In the first one, a class of non-linear systems is determined whose state vector is a memoryless transformation of the state vector of a linear system. The second method considers the generalized Fokker–Planck (Kolmogorov-forward) equation. Non-linear system functions are identified such that the stationary solution of the system admits a prescribed stationary probability density function. Both methods make use of the stochastic integro-differential equations approach. This approach seems to have some computational advantages for the determination of exact stationary probability density functions when compared to the stochastic differential equations approach.

Stochastic linearization of dynamical systems under parametric Poisson white noise excitation

Abstract Several stochastic linearization techniques are derived for nonlinear systems under parametrical Poisson white noise excitation. The differential equations for the first and second order moments of the linearized systems are obtained and differences to the corresponding moment equations of the nonlinear system are discussed. It is shown that different linear models may lead to ‘true’ linearization coefficients in the sense of Kozin in: F. Ziegler, G.I. Schueller (Eds.), Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamic Engineering Systems, Springer, Berlin, Heidelberg, New York, 1988, pp. 45–56. For the Duffing oscillator and the van der Pol oscillator, the results are compared with Monte Carlo simulation.

Equivalent linearization of MDOF systems under external Poisson white noise excitation

Equivalent linearization (EQL) techniques are developed and evaluated for multidimensional systems under external Poisson white noise excitation. Especially, a simulation strategy for the calculation of the linearization coefficients is proposed. The methods are illustrated by several examples that have been treated under Gaussian white noise excitation in the literature. It is shown that EQL for MDOF systems under Poisson white noise excitation is able to deal with problems of nearly the same dimension as under Gaussian white noise excitation.

Parallel processing in computational stochastic dynamics

Abstract Studying large complex problems that often arise in computational stochastic dynamics (CSD) demands significant computer power and data storage. Parallel processing can help meet these requirements by exploiting the computational and storage capabilities of multiprocessing computational environments. The challenge is to develop parallel algorithms and computational strategies that can take full advantage of parallel machines. This paper reviews some of the characteristics of parallel computing and the techniques used to parallelize computational algorithms in CSD. The characteristics of parallel processor environments are discussed, including parallelization through the use of message passing and parallelizing compilers. Several applications of parallel processing in CSD are then developed: solutions of the Fokker–Planck equation, Monte Carlo simulation of dynamical systems, and random eigenvector problems. In these examples, parallel processing is seen to be a promising approach through which to resolve some of the computational issues pertinent to CSD.

The Wong–Zakai theorem for dynamical systems with parametric Poisson white noise excitation

Abstract The theorem of Wong and Zakai is applied to obtain a mathematical model for systems under random impulse excitation, in case that the excitation process tends to be delta-correlated. By means of the Wong–Zakai transformation, a class of reducible non-linear stochastic integro-differential equations is identified. Exact stationary probability density functions for reducible stochastic integro-differential equations are calculated.

On reliability and sensitivity methods for vehicle systems under stochastic crosswind loads

This paper deals with the probabilistic investigation of the crosswind stability of ground vehicles with a strong focus on railway vehicle dynamics. The turbulent crosswind excitation is reduced to an artificial gust model, which is based on the so-called constrained simulation concept and where the gust amplitude, the gust duration and the aerodynamic coefficients of the vehicle are considered as random variables. The railway vehicle is simulated as a nonlinear multi-body vehicle model. Because of the random variables, a probabilistic analysis of the system has to be performed, including a reliability analysis to compute the overturning probability and including a sensitivity analysis concerning the random variables and the parameters of the probability density functions of the random variables.

Bifurcation Analysis of a Turbocharger Rotor Supported by Floating Ring Bearings

Today, rotors of high-speed turbochargers are commonly supported by floating ring bearings due to their low costs and reduced power losses. A well known effect of such rotor bearing-systems is the occurrence of self-excited vibrations. In order to study the different nonlinear vibration effects with the methods of numerical continuation, a perfectly balanced flexible turbocharger rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. After deriving the equations of motion of the turbocharger rotor, bifurcation analyses are carried out with both rigid and flexible model. Thereby, the main focus of the investigation is on the limit-cycle oscillation of higher amplitudes, which may cause rotor damage.In the lower speed range of operation the equilibrium position of the turbocharger rotor becomes unstable by a Hopf bifurcation emerging limit-cycle oscillations. By increasing the rotor speed the limit-cycle may lose its stability by a torus bifurcations leading into an area of quasi-periodic vibrations of the system. Further torus bifurcations, which emanate stable limit-cycles again, and various jump phenomena are also observed. For higher speed ranges a saddle-node bifurcation may occur from which stable limit-cycle oscillations of high amplitudes arise. The rotor speed, where this saddle-node bifurcation takes place, may be defined as a nonlinear critical speed of the turbocharger system supported by floating ring bearings. In the range of the nonlinear critical speed the bifurcation behavior of the turbocharger in floating ring bearings is quite complicated, since a further stable solution coexists beside the critical limit-cycle oscillation.

A probabilistic approach for assessing the crosswind stability of ground vehicles

This paper introduces a risk assessment procedure for the crosswind stability of ground vehicles. A random variable gust model is combined with constrained simulation techniques and variance reducing Monte Carlo methods for an efficient computation of failure probabilities. Based on the failure probability, sensitivities, the influence of additional effects such as turbulence, track irregularities or the friction coefficient between wheel and road can be investigated on an objective basis. Moreover, the procedure allows us to compute the failure probabilities for vehicle journeys or a whole line.