Computational Mechanics

, Volume 63, Issue 1, pp 23–33 | Cite as

A mortar formulation including viscoelastic layers for vibration analysis

  • Alexander PaoliniEmail author
  • Stefan Kollmannsberger
  • Ernst Rank
  • Thomas Horger
  • Barbara Wohlmuth
Original Paper


In order to reduce the transfer of sound and vibrations in structures such as timber buildings, thin elastomer layers can be embedded between their components. The influence of these elastomers on the response of the structures in the low frequency range can be determined accurately by using conforming hexahedral finite elements. Three-dimensional mesh generation, however, is yet a non-trivial task and mesh refinements which may be necessary at the junctions can cause a high computational effort. One remedy is to mesh the components independently from each other and to couple them using the mortar method. Further, the hexahedral mesh for the thin elastomer layer itself can be avoided by integrating its elastic behavior into the mortar formulation. The present paper extends this mortar formulation to take damping into account such that frequency response analyses can be performed more accurately. Finally, the proposed method is verified by numerical examples.


Mortar method Weak coupling High-order finite elements Vibrations Viscoelasticity 



The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) under Grants RA-624/21-2, WO-671/11-1 and WO-671/13-2. They are also thankful to Getzner Werkstoffe GmbH for providing the values of material parameters.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Paolini
    • 1
    Email author
  • Stefan Kollmannsberger
    • 1
  • Ernst Rank
    • 1
    • 2
  • Thomas Horger
    • 3
  • Barbara Wohlmuth
    • 3
  1. 1.Chair for Computation in EngineeringTechnical University of MunichMunichGermany
  2. 2.Institute for Advanced StudyTechnical University of MunichGarchingGermany
  3. 3.Institute for Numerical MathematicsTechnical University of MunichGarchingGermany

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