TY - GEN

T1 - Approximate Solution of the Fokker-Planck Equation for a Multi-Degree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

AU - Förster, Alwin

AU - Panning-von Scheidt, Lars

AU - Wallaschek, Jörg

N1 - Publisher Copyright: Copyright © 2018 by ASME. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/8/30

Y1 - 2018/8/30

N2 - Bladed Disks are subjected to different types of excitations, which cannot in any case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees of freedom and use computational expensive methods, like finite element method (FEM) or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the FOKKER-PLANCK equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical GALERKINtype method to a frictionally damped bladed disk under influence of GAUSSIAN white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte-Carlo Simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

AB - Bladed Disks are subjected to different types of excitations, which cannot in any case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees of freedom and use computational expensive methods, like finite element method (FEM) or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the FOKKER-PLANCK equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical GALERKINtype method to a frictionally damped bladed disk under influence of GAUSSIAN white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte-Carlo Simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

UR - http://www.scopus.com/inward/record.url?scp=85054144566&partnerID=8YFLogxK

U2 - 10.1115/GT2018-75755

DO - 10.1115/GT2018-75755

M3 - Conference contribution

SN - 978-0-7918-5113-5

VL - 7A

T3 - Proceedings of the ASME Turbo Expo

BT - Proceedings of the ASME Turbo Expo: Turbomachinery Technical Conference and Exposition - 2018

T2 - ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, GT 2018

Y2 - 11 June 2018 through 15 June 2018

ER -