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Pattern optimization of intentional blade mistuning for the reduction of the forced response using genetic algorithm

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Abstract

This paper investigates how intentional mistuning of bladed disks reduces their sensitivity to unintentional random mistuning. The class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say). A two-step procedure is then described to optimize the arrangement of these blades around the disk to reduce the effects of unintentional random mistuning. First, a pure optimization effort is undertaken to obtain the pattern (s) of the A and B blades that yields small/the smallest value of the largest amplitude of response to a given excitation in the absence of unintentional random mistuning using Genetic Algorithm. Then, in the second step, a qualitative/quantitative estimate of the sensitivity for the optimized intentionally mistuned bladed disks with respect to unintentional random mistuning is performed by analyzing their amplification factor, probability density function and passband/stopband structures. Examples of application with simple bladed disk models demonstrate the significant benefits of using this class of intentionally mistuned disks.

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Abbreviations

A:

Mistuned blade having natural frequencies 5% lower than tuned one

A i max :

Maximum amplitude of blade response on diski

B:

Mistuned blade having natural frequencies 5% higher than tuned one

C:

Tuned blade

c :

Damping coefficient of blade (N-s/m)

F o :

Magnitude of exciting force (N)

g :

Generation number of genetic algorithm

g max :

Maximum number of generation

k c :

Coupling stiffness in blade-to-blade (N/m)

k t :

Stiffness of blade (N/m)

m t :

Blade mass (kg)

N :

Total number of blades

n pop :

Population number of genetic algorithm

P c :

Crossover probability

p m :

Mutation probability

ps(i):

Selection probability

r :

Exciting engine order

σ :

Standard deviation of unintentional random mistuning

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Correspondence to ByeongKeun Choi.

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Choi, B. Pattern optimization of intentional blade mistuning for the reduction of the forced response using genetic algorithm. KSME International Journal 17, 966–977 (2003). https://doi.org/10.1007/BF02982981

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Key Words

  • Intentional Mistuning
  • Unintentional Random Mistuning
  • Monte Simulation
  • Probability Density Function
  • Passband/Stopband Structure Carlo