Computing elliptic membrane high frequencies by Mathieu and Galerkin methods

Autor:	Robert W. Scharstein, Howard B. Wilson
Rok vydání:	2006
Předmět:	Series (mathematics) General Mathematics Mathematical analysis General Engineering Solver symbols.namesake Mathieu function Discontinuous Galerkin method Special functions Neumann boundary condition symbols Galerkin method Eigenvalues and eigenvectors Mathematics
Zdroj:	Journal of Engineering Mathematics. 57:41-55
ISSN:	1573-2703 0022-0833
DOI:	10.1007/s10665-006-9070-1
Popis:	Resonant modes of an elliptic membrane are computed for a wide range of frequencies using a Galerkin formulation. Results are confirmed using Mathieu functions and finite-element methods. Algorithms and their implementations are described to handle Dirichlet or Neumann boundary conditions and draw animations or contour plots of the modal surfaces. The methods agree to four or more digit accuracy for the first one hundred modes. The effects of high function order and high frequency parameter upon the convergence of the modified Mathieu function series are discussed and quantified. The Galerkin method is conceptually simple and requires only an eigenvalue solver without the need of special functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::660b668adea621821f866d582559211e https://doi.org/10.1007/s10665-006-9070-1 Zobrazit plný text záznamu Full text from SpringerLink