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Research Papers

# Minimizing Maximum Modal Force in Mistuned Bladed Disk Forced Response

[+] Author and Article Information
Keith W. Jones

Propulsion Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433

J. Turbomach 130(1), 011011 (Jan 25, 2008) (11 pages) doi:10.1115/1.2749291 History: Received September 16, 2003; Revised January 11, 2007; Published January 25, 2008

## Abstract

Amplitude magnification is defined as the maximum forced response amplitude of any blade on a mistuned bladed disk divided by the maximum response amplitude of any blade on a tuned bladed disk over a range of engine order excitation frequencies. This paper shows that amplitude magnification can be approximated as the maximum ratio of modal force divided by modal vector magnitude in an isolated family of turbine engine bladed disk modes. An infinite linear mistuning pattern, defined by a constant interblade stiffness increment between an infinite number of blades, is found to minimize the maximum modal force when subjected to engine order N/4 excitation. Linear mistuning, an approximation of the infinite linear mistuning pattern, approximately minimizes the maximum modal force for bladed disks with a finite number of blades when subjected to engine order N/4 excitation. From this theory, $2/N$ is proposed to be a lower boundary for amplitude magnification. The linear mistuning method is demonstrated to produce very low amplitude magnifications numerically and experimentally. The numerical examples suggest that linear mistuning may produce amplitude magnifications near the absolute minimum possible.

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## Figures

Figure 6

Effect of the engine order on the forced response of the linearly mistuned spring mass model (A=0.0736)

Figure 7

Probability density function of spring mass model amplitude magnifications (E=N∕4)

Figure 8

Comparison of linear and numerically optimized mistuning from the spring mass model (E=N∕4)

Figure 9

Amplitude magnification contours for various combinations of coupling and linear mistuning (g* plotted for ζ→0, E=N∕4)

Figure 1

Infinite linear mistuning and its truncated approximation

Figure 2

Spring mass model

Figure 3

Amplitude magnification versus normalized linear mistuning amplitude for the spring mass model (E=N∕4)

Figure 4

Forced response of the spring mass model (E=N∕4, A=0.0736)

Figure 5

Linearly mistuned spring mass model modes (A=0.0736)

Figure 10

Amplitude magnification contours for various combinations of numbers of blades and linear mistuning (g* plotted for ζ→0, E=N∕4)

Figure 11

Estimates of the minimum amplitude magnification for the spring mass model (g* plotted for ζ→0, E=N∕4)

Figure 12

FEM of a realistic bladed disk

Figure 14

Linear mistuning experimental setup

Figure 15

Predicted amplitude magnification versus normalized linear mistuning amplitude (E=4)

Figure 13

Forced response of the linearly mistuned bladed disk FEM (E=N∕4, ζ=0.001, A=0.0289)

Figure 16

Linear mistuning experimental results (E=4)

## Errata

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