Response Statistics and Reliability Analysis of a Mistuned and Frictionally Damped Bladed Disk Assembly Subjected to White Noise Excitation

2010 ◽  
Author(s):  
Pankaj Kumar ◽  
S. Narayanan
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Forced Response ◽  
Computationally Efficient ◽  
Bladed Disk ◽  
White Noise Excitation ◽  
Bladed Disk Assembly ◽  
Mean Square Response

In the design of gas turbine engines, the analysis of nonlinear vibrations of mistuned and frictionally damped blade-disk assembly subjected to random excitation is highly complex. The transitional probability density function (PDF) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents important improvement and extensions to a computationally efficient higher order, finite difference (FD) technique for the solution of higher dimensional FP equation corresponding to a two degree of freedom nonlinear system representative of vibration of tip shrouded frictionally damped bladed disk assembly subjected to Gaussian white noise excitation. Effects of friction damping on the mean square response of a blade are investigated. The friction coefficient of the damper is assumed to be a function of the sliding velocity of the contact surface. The effects of stiffness and damping mistuning on the forced response of frictionally damped bladed disk are investigated. Numerical studies are presented for a pair of mistuned blades of cyclic assemblies. The response and reliability of a blade subjected to random excitation is also obtained. With time averaged probability density as an invariant measure, the probability of large excursion in case of damping mistuning is also presented. The results of the FD method are validated by comparing with Monte Carlo Simulation (MCS) results.

The Response Statistics, Jump and Bifurcation of Nonlinear Dynamical Systems Subjected to White Noise and Combined Sinusoidal and White Noise Excitation

2007 ◽  
Author(s):  
Pankaj Kumar ◽  
S. Narayanan
Keyword(s):  
Nonlinear Systems ◽  
White Noise ◽  
Nonlinear Dynamical Systems ◽  
Gaussian White Noise ◽  
Nonlinear Dynamical ◽  
White Noise Excitation ◽  
Bladed Disk Assembly ◽  
Noise Frequency ◽  
System Nonlinearity ◽  
Non Gaussian

The prediction of the response of nonlinear systems subjected to stochastic parametric, narrowband and wideband or coloured external excitation is of importance in the field of structural and rotor dynamics. The transitional probability density function (pdf) for the random response of nonlinear systems under white or coloured 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 FP equation for the pdf of response for general nonlinear systems subjected to external white noise and combined sinusoidal and white noise excitation. The effect of intensity of white noise, frequency and amplitude of sinusoidal excitation and level of system nonlinearity on the non-Gaussian nature of response caused by the system nonlinearity are investigated. Stochastic behaviours like stability, jump, bifurcation are examined as the system parameters change. The finite element (FE) scheme is used to solve the FP equation and obtain the statistics of a two degree-of-freedom linear system representative of the vibration of gas turbine tip-shrouded bladed disk assembly subjected to Gaussian white noise excitation as an illustrative example.

Optimal Design of Coupled Structures Subjected to Random Excitation

1995 ◽  
Author(s):  
Arun M. Sampath ◽  
C. Nataraj ◽  
H. Ashrafiuon
Keyword(s):  
White Noise ◽  
Random Excitation ◽  
Beam Model ◽  
Mean Square ◽  
White Noise Excitation ◽  
Design Variables ◽  
Mean Square Response ◽  
Coupled Structures ◽  
Band Limited ◽  
Stiffness And Damping

Abstract This paper presents optimization of the response of coupled structures subjected to random excitation. The dynamic system involves discrete and continuous models of coupled structures. The structures are assumed to be subjected to white noise excitation of known power spectral density. The mean square response of the structure is taken as the objective function. The physical properties such as length, thickness, stiffness and damping are taken as the design variables. The discrete system is assumed to be subjected to two kinds of excitation; band-limited white noise excitation and ideal white noise excitation. Coupling stiffness and damping characteristics are used as design variables. For the case of continuous coupled beam model, band-limited white noise excitation is considered and the root mean square response of the structure is minimized for a range of excitation frequency. Geometric properties of the structure are used as design variables.

Statistics of Response of a Mistuned Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitation

1998 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Analytical Methods ◽  
Narrow Band ◽  
Analytical Techniques ◽  
Dominant Frequency ◽  
Random Excitation ◽  
Structural Coupling ◽  
Bladed Disk ◽  
Bladed Disk Assembly

This paper deals with the statistics of the response of a mistuned bladed disk assembly subjected to random excitation. Analytical techniques are developed to compute this statistics for two types of random excitation: white noise and narrow band. The validity of the analytical methods has been established by comparison with the results from numerical simulations. The sensitivities of the response to mistuning have been examined as a function of the width of the frequency band of the random excitation, the dominant frequency of the random excitation and the structural coupling between adjacent blades.

Statistics of Response of a Mistuned Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitation

1999 ◽  
Vol 121 (4) ◽  
pp. 710-717 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Analytical Methods ◽  
Narrow Band ◽  
Analytical Techniques ◽  
Dominant Frequency ◽  
Random Excitation ◽  
Structural Coupling ◽  
Bladed Disk ◽  
Bladed Disk Assembly

This paper deals with the statistics of the response of a mistuned bladed disk assembly subjected to random excitation. Analytical techniques are developed to compute this statistics for two types of random excitation: white noise and narrow band. The validity of the analytical methods has been established by comparison with the results from numerical simulations. The sensitivities of the response to mistuning have been examined as a function of the width of the frequency band of the random excitation, the dominant frequency of the random excitation and the structural coupling between adjacent blades.

Statistics of Responses of a Mistuned and Frictionally Damped Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitations

2000 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
White Noise ◽  
Narrow Band ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Dampers ◽  
Analytical Technique ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

In this paper, the effects of friction dampers on the vibration of a mistuned bladed disk assembly are examined for the following types of random excitation: white noise and narrow band. To compute the statistics of nonlinear response, an analytical technique is developed based on the equivalent linearization method. The validity of the analytical technique has been established by comparison with the results from numerical simulations. The relation between the vibration mode of the system and the performance of friction dampers is investigated.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

The Effect of Non-Uniform Aerodynamic Loading on the Blade Responses

2007 ◽  
Author(s):  
Abdelgadir M. Mahmoud ◽  
Mohd S. Leong
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Flow Section ◽  
Flow Distortion ◽  
Inlet Flow ◽  
Bladed Disk ◽  
Aerodynamic Loading ◽  
Bladed Disk Assembly ◽  
Flow Generator ◽  
Inlet Flow Distortion

Turbine blades are always subjected to severe aerodynamic loading. The aerodynamic loading is uniform and Of harmonic nature. The harmonic nature depends on the rotor speed and number of nozzles (vanes counts). This harmonic loading is the main sources responsible for blade excitation. In some circumstances, the aerodynamic loading is not uniform and varies circumferentially. This paper discussed the effect of the non-uniform aerodynamic loading on the blade vibrational responses. The work involved the experimental study of forced response amplitude of model blades due to inlet flow distortion in the presence of airflow. This controlled inlet flow distortion therefore represents a nearly realistic environment involving rotating blades in the presence of airflow. A test rig was fabricated consisting of a rotating bladed disk assembly, an inlet flow section (where flow could be controlled or distorted in an incremental manner), flow conditioning module and an aerodynamic flow generator (air suction module with an intake fan) for investigations under laboratory conditions. Tests were undertaken for a combination of different air-flow velocities and blade rotational speeds. The experimental results showed that when the blades were subjected to unsteady aerodynamic loading, the responses of the blades increased and new frequencies were excited. The magnitude of the responses and the responses that corresponding to these new excited frequencies increased with the increase in the airflow velocity. Moreover, as the flow velocity increased the number of the newly excited frequency increased.

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