In turbomachinery, the analysis of systems subjected to stochastic or periodic excitation becomes highly complex in the presence of nonlinearities. Nonlinear rotor systems exhibit a variety of dynamic behaviors that include periodic, quasiperiodic, chaotic motion, limit cycle, jump phenomena, etc. The transitional probability density function (PDF) for the random response of nonlinear systems under white or colored noise excitation (delta-correlated) is governed by both the forward Fokker–Planck (FP) and backward Kolmogorov equations. This paper presents efficient numerical solution of the stationary and transient form of the forward FP equation corresponding to two state nonlinear systems by standard sequential finite element (FE) method using shape functions and Crank–Nicholson time integration scheme. For computing the reliability of system, the transient FP equation is solved on the safe domain defined by D barriers using the FE method. A new approach for numerical implementation of path integral (PI) method based on non-Gaussian transition PDF and Gauss–Legendre scheme is developed. In this study, PI solution procedure is employed to solve the FP equation numerically to examine some features of chaotic and stochastic responses of nonlinear rotor systems.
Skip Nav Destination
Article navigation
January 2009
Research Papers
Nonlinear Stochastic Dynamics, Chaos, and Reliability Analysis for a Single Degree of Freedom Model of a Rotor Blade
Pankaj Kumar,
Pankaj Kumar
Gas Turbine Design Department,
Bharat Heavy Electricals Limited
, Hyderabad-502032, India
Search for other works by this author on:
S. Narayanan
S. Narayanan
Department of Mechanical Engineering,
Indian Institute of Technology Madras
, Chennai-600036, India
Search for other works by this author on:
Pankaj Kumar
Gas Turbine Design Department,
Bharat Heavy Electricals Limited
, Hyderabad-502032, India
S. Narayanan
Department of Mechanical Engineering,
Indian Institute of Technology Madras
, Chennai-600036, IndiaJ. Eng. Gas Turbines Power. Jan 2009, 131(1): 012506 (8 pages)
Published Online: October 13, 2008
Article history
Received:
April 3, 2008
Revised:
April 4, 2008
Published:
October 13, 2008
Citation
Kumar, P., and Narayanan, S. (October 13, 2008). "Nonlinear Stochastic Dynamics, Chaos, and Reliability Analysis for a Single Degree of Freedom Model of a Rotor Blade." ASME. J. Eng. Gas Turbines Power. January 2009; 131(1): 012506. https://doi.org/10.1115/1.2967720
Download citation file:
Get Email Alerts
Shape Optimization of an Industrial Aeroengine Combustor to reduce Thermoacoustic Instability
J. Eng. Gas Turbines Power
Dynamic Response of A Pivot-Mounted Squeeze Film Damper: Measurements and Predictions
J. Eng. Gas Turbines Power
Review of The Impact Of Hydrogen-Containing Fuels On Gas Turbine Hot-Section Materials
J. Eng. Gas Turbines Power
Effects of Lattice Orientation Angle On Tpms-Based Transpiration Cooling
J. Eng. Gas Turbines Power
Related Articles
Modified Path Integral Solution of Fokker–Planck Equation: Response and Bifurcation of Nonlinear Systems
J. Comput. Nonlinear Dynam (January,2010)
Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors
J. Appl. Mech (June,1996)
Adjoint Harmonic Sensitivities for Forced Response Minimization
J. Eng. Gas Turbines Power (January,2006)
Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems Under Poisson White Noise Excitation
J. Appl. Mech (March,2011)
Related Proceedings Papers
Related Chapters
STRUCTURAL RELIABILITY ASSESSMENT OF PIPELINE GIRTH WELDS USING GAUSSIAN PROCESS REGRESSION
Pipeline Integrity Management Under Geohazard Conditions (PIMG)
Introduction I: Role of Engineering Science
Fundamentals of heat Engines: Reciprocating and Gas Turbine Internal Combustion Engines
Hydraulic Turbomachines
Mechanical Energy Conversion: Exercises for Scaling Renewable Energy Systems