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Response of large mistuned bladed disk assembly subjected to random excitations

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Abstract

In this study, the effects of large geometric mistuning on blade response are investigated considering the change of mistuning properties and excitation characteristics. The response variations because of large mistuning are negligible under white noise excitations and are highly significant under narrow band excitations. For the different excitation correlations, the responses are represented using non-dimensional variables in order for the results to be comparable to each other. It is shown that the ratio of the modal frequency between the tuned and large mistuned blades determines the propagation direction of the natural frequencies of the mistuned system, therefore, the responses of large mistuned blades depend primarily on their level of modal frequency.

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Abbreviations

A :

System matrix

B :

System matrix

C :

Damping of blade system

C F :

Damping of band-pass filter

C R :

Coupled structure of band-pass filter

c :

Damping coefficient of each blade

E[ ]:

Expected value

F(t):

External force

g(t):

Narrow band excitation

I n :

Identity matrix

K :

Stiffness of blade system

K c :

Coupling stiffness

K F :

Stiffness of band-pass filter

k t :

Stiffness of tuned blade

k d :

Large mistuning value for stiffness

k i :

Stiffness of ith blade

δk di :

Deviations in stiffness because of large mistuning

δk ti :

Deviations in stiffness because of small mistuning

l :

Number of large mistuned blades

M :

Mass matrix of system model

δM :

Perturbation of mass

m t :

Mass of tuned blade

m d :

Large mistuning value for mass

m i :

Mass of ith blade

δm di :

Deviations in mass because of large mistuning

δm ti :

Deviations in mass because of small mistuning

n :

Number of blades

P o :

Correlation matrix of tuned system

P n :

Correlation matrix of zn

P w :

Correlation matrix of zw

Q 0 :

Intensity of white noise excitations

R g :

Correlation matrix of g(t )

R w :

Correlation matrix of w(t )

R xt :

Response variance of tuned system

w(t ):

White noise excitation

x i :

Displacement of ith blade

z :

State vector

σ Ri :

Standard deviation of response variance of ith blade

μ Ri :

Mean of response variance of ith blade

ξ F :

Damping ratio of band-pass filter

ω F :

Dominant frequency of narrow band excitation

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Acknowledgments

This work was supported by the research fund of Korea University of Technology & Education in 2017, Korea.

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Authors and Affiliations

  1. Department of Mechanical Design Engineering, Korea University of Technology & Education, Chungjeolro 1600, Dongnam-gu, Cheonan, 31253, Korea

    Douksoon Cha

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  1. Douksoon Cha
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Correspondence to Douksoon Cha.

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Recommended by Editor No-cheol Park

Douksoon Cha is a Professor of the Korea University of Technology & Education, Cheonan, Korea. He received his Ph.D. in Mechanical Engineering from Pennsylvania State University. His research interests include vibration of turbine blade, friction damper and nonlinear dynamics.

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Cha, D. Response of large mistuned bladed disk assembly subjected to random excitations. J Mech Sci Technol 34, 603–615 (2020). https://doi.org/10.1007/s12206-020-0108-5

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  • DOI: https://doi.org/10.1007/s12206-020-0108-5

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