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A Comparison of Two Reduction Techniques for Forced Response of Shrouded Blades with Contact Interfaces

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Dynamics of Coupled Structures, Volume 4

Abstract

Two reduction methods for dynamic analysis of structures with local nonlinearity are compared. Dual and primal formulation have the same projection basis including flexibility residual attachment modes and free interface modes, but there are significant differences in their implementation. Both methods can be applied to nonlinear forced response analysis of turbine blades with contact interfaces in shroud. In this study, the shroud contact elements are employed using the adequate description of friction and 3D tangential coupled contact forces considering the effect of normal load variation. In order to examine and compare the accuracy of the two formulations, a rod and a simplified shrouded turbine blade was considered as case studies.

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Abbreviations

[M],[C], and [K]:

Mass, damping, and stiffness matrix

X, F :

Displacement and Force vector

[Φ]:

Matrix of free interface dynamic modes

[Ψ], [Ψ]ar :

Matrix of attachment modes and residual attachment modes

ωp and Φp :

pth eigenvalue and eigenvectors of free interface body

∗N and ∗L :

Pertaining to nonlinear(interface) and linear(inner) dofs of substructure

R :

Reduction matrix

h :

Harmonic Component Number

α :

Mass proportional damping

∗C and ∗E :

Pertaining to Contact and excitation

\( {{\bar{\mathrm{X}}}}^{\mathrm{h}} \) :

Vector of Fourier coefficient of hth harmonic of X

ω :

Circular frequency

∗n :

Pertaining to nth contact nodes

[\( \tilde{\mathrm{A}} \)]:

Pertaining to characteristic matrix [A] of system with interfaces added stiffness in fully suck condition

[kc, n]:

nth sub matrix regarding the added stiffness to nth contact node

kt, kn :

Tangential and normal contact stiffness parameters

α :

Proportional damping constant

N0 :

Static normal preload on contact area

References

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran

    Fahimeh Mashayekhi & Ali Salehzadeh Nobari

  2. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy

    Stefano Zucca

Authors
  1. Fahimeh Mashayekhi
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  2. Stefano Zucca
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  3. Ali Salehzadeh Nobari
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Linnaeus University, Växjö, Sweden

    Andreas Linderholt

  2. Department of Engineering Physics, University of Wisconsin–Madison, Madison, Wisconsin, USA

    Matthew S. Allen

  3. Structural Dynamics Department, Sandia National Laboratory, Albuquerque, New Mexico, USA

    Randall L. Mayes

  4. Lehrstuhl für Angewandte Mechanik, TU München, Garching, Bayern, Germany

    Daniel Rixen

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Mashayekhi, F., Zucca, S., Nobari, A.S. (2018). A Comparison of Two Reduction Techniques for Forced Response of Shrouded Blades with Contact Interfaces. In: Linderholt, A., Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-74654-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-74654-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74653-1

  • Online ISBN: 978-3-319-74654-8

  • eBook Packages: EngineeringEngineering (R0)

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