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 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 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.

Effects of Intentional Large Mistuning to the Performance of B–B Friction Dampers in the Mistuned Bladed Disk Assembly Subjected to Narrow band Random Excitation

2021 ◽  
Author(s):  
Douksoon Cha
Keyword(s):  
Simple Model ◽  
Efficient Method ◽  
Narrow Band ◽  
Random Excitation ◽  
Additional Mass ◽  
Friction Dampers ◽  
Analytical Technique ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Abstract In this study, the effects of intentional mistuning on the performance of B–B friction dampers are investigated in an inherently mistuned bladed disk assembly subjected to narrow band random excitation. The intentional large mistuning and inherent small mistuning are modeled by the additional mass and perturbations in the stiffness of the blade, respectively. It was found that the performance of B–B friction dampers improved owing to the intentional mistuning of the correlated excitations. Based on a simple model of an intentionally and inherently mistuned bladed disk assembly, the analytical technique offers an efficient method to evaluate the effects of intentional mistuning and friction dampers.

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.

Effects of the Nature of Excitation on the Response of a Mistuned Bladed Disk Assembly

2002 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
Narrow Band ◽  
Analytical Techniques ◽  
Bladed Disk ◽  
Engine Order ◽  
Bladed Disk Assembly ◽  
Time Invariant

In this paper, responses of a mistuned bladed disk assembly are examined and compared for three types of excitations: uncorrelated narrow band random excitations, correlated narrow band random excitations and sinusoidal excitations with unknown (time-invariant and random) amplitudes. Analytical techniques are also developed to compute the statistics of responses for these types of excitations. Effects of correlations of narrow band excitations are investigated in details. It has been found that the response statistics for correlated narrow band random excitations can be viewed in terms of the concepts related to the response to a deterministic engine order excitation.

Effects of the Nature of Excitation on the Response of a Mistuned Bladed Disk Assembly

2002 ◽  
Vol 124 (4) ◽  
pp. 588-596 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
Narrow Band ◽  
Analytical Techniques ◽  
Bladed Disk ◽  
Engine Order ◽  
Bladed Disk Assembly ◽  
Time Invariant

In this paper, responses of a mistuned bladed disk assembly are examined and compared for three types of excitations: uncorrelated narrow band random excitations, correlated narrow band random excitations and sinusoidal excitations with unknown (time-invariant and random) amplitudes. Analytical techniques are also developed to compute the statistics of responses for these types of excitations. Effects of correlations of narrow band excitations are investigated in details. It has been found that the response statistics for correlated narrow band random excitations can be viewed in terms of the concepts related to the response to a deterministic engine order excitation.

Equivalent Linearization of Bladed Disk Assemblies with Friction Nonlinearities Under Random Excitation

2020 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Damper ◽  
Bladed Disk ◽  
Stationary Stochastic Processes ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

Abstract The present article addresses the vibrational behaviour of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behaviour. The use of friction dampers for energy dissipation and suppression of large amplitudes makes the mechanical system nonlinear, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from clearly defined deterministic to random excitation. So far, the latter problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The nonlinear contact is modelled both with an elastic Coulomb-slider and a Bouc-Wen formulation to reproduce the hysteretic character of a friction nonlinearity occurring in the presence of a friction damper. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments, do not change over time. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each segment is approximated with several degrees of freedom.

Computation of the Statistics of Forced Response of a Mistuned Bladed Disk Assembly via Polynomial Chaos

2003 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Numerical Simulations ◽  
Polynomial Chaos ◽  
Random Variable ◽  
Forced Response ◽  
Bladed Disk ◽  
Bladed Disk Assembly

The method of polynomial chaos has been used to analytically compute the statistics of forced response of a mistuned bladed disk assembly. The model of the bladed disk assembly considers only one mode of vibration of each blade. Mistuning phenomenon has been simulated by treating the modal stiffness of each blade as a random variable. The validity of the polynomial chaos method has been corroborated by comparison with the results from numerical simulations.

Computation of the Statistics of Forced Response of a Mistuned Bladed Disk Assembly via Polynomial Chaos

2005 ◽  
Vol 128 (4) ◽  
pp. 449-457 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Numerical Simulations ◽  
Polynomial Chaos ◽  
Random Variable ◽  
Forced Response ◽  
Bladed Disk ◽  
Bladed Disk Assembly

The method of polynomial chaos has been used to analytically compute the statistics of the forced response of a mistuned bladed disk assembly. The model of the bladed disk assembly considers only one mode of vibration of each blade. Mistuning phenomenon has been simulated by treating the modal stiffness of each blade as a random variable. The validity of the polynomial chaos method has been corroborated by comparison with the results from numerical simulations.

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