Computational Mechanics

, Volume 52, Issue 5, pp 983–992 | Cite as

Low-complexity computation of plate eigenmodes with Vekua approximations and the method of particular solutions

  • Gilles ChardonEmail author
  • Laurent Daudet
Original Paper


This paper extends the method of particular solutions (MPS) to the computation of eigenfrequencies and eigenmodes of thin plates, in the framework of the Kirchhoff-Love plate theory. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the finite element method, at reduced complexity, and with large flexibility in the implementation choices.


Kirchhoff plate theory Biharmonic equation  Numerical methods Algorithms Eigenvalues 



The authors acknowledge partial support from Agence Nationale de la Recherche (ANR), Project ECHANGE (ANR-08-EMER-006), Project LABEX WIFI (ANR-10-IDEX-0001-02 PSL*), and Austrian Science Fund (FWF) START-Project FLAME (Y 551-N1). LD is on a joint affiliation with Institut Universitaire de France.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut Langevin, UPMC Univ. Paris 06ParisFrance
  2. 2.Acoustics Research Institute, Austrian Academy of SciencesWienAustria
  3. 3.Institut LangevinParis Diderot UniversityParisFrance

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