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Research Papers: Gas Turbines: Structures and Dynamics

# Frequency-Domain Sensitivity Analysis of Stability of Nonlinear Vibrations for High-Fidelity Models of Jointed Structures

[+] Author and Article Information
E. P. Petrov

School of Engineering and Informatics,
University of Sussex,
Brighton BN1 9QT, UK
e-mail: y.petrov@sussex.ac.uk

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 6, 2017; final manuscript received July 9, 2017; published online September 19, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(1), 012508 (Sep 19, 2017) (12 pages) Paper No: GTP-17-1303; doi: 10.1115/1.4037708 History: Received July 06, 2017; Revised July 09, 2017

## Abstract

For the analysis of essentially nonlinear vibrations, it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps, and other types of nonlinear contact interfaces. The method allows using large-scale finite element (FE) models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including friction, gaps, and cubic elastic nonlinearity.

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Topics: Stability

## References

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## Figures

Fig. 1

Amplitude (a) and stability factors (b) of the linear oscillator

Fig. 2

Sensitivities of RSF and ISF with respect to natural frequency and modal damping variations

Fig. 3

The maximum displacement and the stability factors: cubic nonlinearity

Fig. 6

Stability sensitivities ∂λRe/∂ω1 and ∂λRe/∂η1

Fig. 7

Stability sensitivities ∂λIm/∂ω1 and ∂λIm/∂η1

Fig. 8

The maximum displacement and stability factors: gap nonlinearity

Fig. 9

Stability sensitivity ∂λRe/∂kgap

Fig. 10

Stability sensitivity ∂λRe/∂gap

Fig. 11

Dependency of the maximum displacement and stability factors on excitation frequency: friction contact

Fig. 4

Stability sensitivity ∂λRe/∂k3

Fig. 5

Stability sensitivity ∂λIm/∂k3

Fig. 23

Stability sensitivity ∂λIm/∂k3

Fig. 24

Stability sensitivity ∂λRe/∂ωj for different modes

Fig. 25

Stability sensitivity ∂λRe/∂ηj for different modes

Fig. 15

Selected stability factors for the block with cubic nonlinearity: effect of the number of mode shapes

Fig. 16

Stability sensitivity ∂λRe/∂k3

Fig. 17

Stability sensitivity ∂λRe/∂ω1

Fig. 18

Stability sensitivity ∂λRe/∂η1

Fig. 19

A cooled turbine blade: a FE model

Fig. 20

Amplitudes of the turbine blade nonlinear response

Fig. 12

Stability sensitivity ∂λRe/∂μ

Fig. 13

Stability sensitivity ∂λRe/∂kt

Fig. 14

Amplitudes of a beam with cubic nonlinearity

Fig. 21

Stability factors of the turbine blade

Fig. 22

Stability sensitivity ∂λRe/∂k3

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