A boundary element method for eigenvalue problems of polygonal membranes and plates
type: Item
instance of: scholarly article
title: A boundary element method for eigenvalue problems of polygonal membranes and plates
zbMATH Open document ID: 0606.73099
DOI: 10.1007/BF01184282
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: An advanced boundary element formulation for eigenvalue problems of membranes and plates is developed. Polygonal membranes are considered, and are embedded into a proper basic domain in order to satisfy boundary conditions exactly as far as possible. Hence, boundary integrals have to be applied at the not coinciding boundaries only. Eigenvalues of the underlying Dirichlet's Helmholtz problem are calculated from frequency response functions evaluated by that ''method with Green functions of finite domains'', and natural frequencies of corresponding membranes and simply supported plates are determined by analogy. A numerical investigation is performed for parallelogram Mindlin plates. Natural frequencies and critical buckling eigenvalues are graphically represented in a nondimensional form, where the influence of skew angle and plate thickness is studied.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 3980678
zbMATH Keywords: advanced boundary element formulation
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: Polygonal membranes
zbMATH Keywords: Dirichlet's Helmholtz problem
zbMATH Keywords: frequency response functions
zbMATH Keywords: Green functions
zbMATH Keywords: finite domains
zbMATH Keywords: natural frequencies
zbMATH Keywords: simply supported plates
zbMATH Keywords: parallelogram Mindlin plates
zbMATH Keywords: critical buckling eigenvalues
author: R. Heuer
author: H. Irschik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3980678