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Research Papers

A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

[+] 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

Manuscript received June 22, 2018; final manuscript received June 30, 2018; published online October 29, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(3), 031023 (Oct 29, 2018) (11 pages) Paper No: GTP-18-1301; doi: 10.1115/1.4040850 History: Received June 22, 2018; Revised June 30, 2018

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when (i) the design parameters characterize the properties of nonlinear contact interfaces (e.g., gap, contact stiffness, and friction coefficient); (ii) the design parameters describe linear components of the analyzed structure (e.g., parameters of geometric shape, material, natural frequencies, and modal damping); and (iii) these parameters describe the excitation loads (e.g., their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees-of-freedom (DOF). The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element (FE) models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

Copyright © 2019 by ASME
Topics: Stability
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References

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Figures

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Fig. 1

Examples of the parameter variation trajectories: (a) three-dimensional trajectory and (b) two-dimensional trajectory

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Fig. 2

Forced response and the stability boundary: a case of 1DOF system with cubic nonlinearity

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Fig. 3

The amplitude and frequency values at stability loss as a function of cubic stiffness

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Fig. 4

Forced response and the stability boundary: variation of gap stiffness for 1DOF system

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Fig. 5

The amplitude and frequency values at stability loss as a function of gap stiffness value

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Fig. 6

Forced response and the stability boundary: variation of gap value for 1DOF system

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Fig. 7

The amplitude and frequency values at stability loss as a function of gap value

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Fig. 8

The amplitude (a) and frequency (b) values at stability loss as a function of two contact interface parameters

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Fig. 9

Forced response and the stability boundary: a case of beam with cubic nonlinearity

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Fig. 10

The amplitude and frequency values at stability loss as a function of cubic stiffness

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Fig. 11

The forced response amplitude for a beam with gap nonlinearity: kgap=105 and g=0.1

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Fig. 12

The trajectories of all Floquet multipliers for the whole range of the excitation frequency variation

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Fig. 13

Forced responses obtained by the time-domain integration and by the multiharmonic balance method

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Fig. 14

Forced response and the parametric stability boundary analysis: variation of gap value

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Fig. 15

Time integration and MHB method for the isolated solution branch, gap = 0.05

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Fig. 16

The amplitude and frequency values at stability loss as a function of gap value

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Fig. 17

Forced response and the parametric stability boundary analysis: variation of gap stiffness

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Fig. 18

The amplitude and frequency values at stability loss as a function of gap stiffness

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Fig. 19

A cooled turbine blade: a FE model

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Fig. 20

Forced response and the stability boundary analysis: the variation of cubic stiffness for turbine blade

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Fig. 21

The amplitude and frequency values at stability loss as a function of cubic stiffness for turbine blade

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Fig. 22

Variation of all stability factors along the stability loss solution trajectory

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