Computing and Visualization in Science

, Volume 19, Issue 5–6, pp 77–89 | Cite as

A nonlinear eigenmode solver for linear viscoelastic structures

  • Clemens PechsteinEmail author
  • Stefan Reitzinger
Original Article


This article deals with the nonlinear eigenvalue problem originating from the finite element discretization of mechanical structures involving linear viscoelastic material. The material function is assumed to be positive real, which allows a location of the eigenvalues in the left complex half space of the Laplace domain. The solution method for the considered nonlinear eigenvalue problem is based on the contour integral method, where special focus is put on the efficient numerical computation of the linear system along the boundary of the given search area. For this purpose, the reduced order model technique is used and appropriate a priori error estimates are provided. Finally, the validity of the proposed method is illustrated in numerical examples.


Nonlinear eigenvalue problem Linear viscoelastic material Contour integral method Reduced order model Laplace domain 



We would like to thank the anonymous referees for their valuable comments that helped to improve our paper.


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Copyright information

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

Authors and Affiliations

  1. 1.CST – Computer Simulation Technology GmbH, a Dassault Systèmes CompanyDarmstadtGermany

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