Analytical and numerical investigation for true and spurious eigensolutions of an elliptical membrane using the real-part dual BIEM/BEM

DOI10.1007/s11012-011-9496-zzbMath1293.74167OpenAlexW2046393269MaRDI QIDQ399261

Jeng-Tzong Chen, Jia-Wei Lee, Shyue-Yuh Leu

Publication date: 19 August 2014

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11012-011-9496-z

zbMATH Keywords

eigensolutionsMathieu functionsdegenerate kernelelliptical coordinatesJacobian term

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Boundary element methods applied to problems in solid mechanics (74S15) Membranes (74K15)

Related Items (3)

Eigenproblems of two-dimensional acoustic cavities with smoothly varying boundaries by using the generalized multipole method ⋮ Eigenanalysis for a confocal prolate spheroidal resonator using the null-field BIEM in conjunction with degenerate kernels ⋮ Free vibration analysis of an elliptical plate with eccentric elliptical cut-outs

Uses Software

• LINPACK
• ABAQUS

Cites Work

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• Analytical study and numerical experiments of true and spurious eigensolutions of free vibration of circular plates using real-part BIEM
• On the spurious eigensolutions for the real-part boundary element method
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• Mathematical analysis and numerical study of true and spurious eigenequations for free vibration of plates using real-part BEM
• Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary.
• NULL-FIELD INTEGRAL EQUATION APPROACH FOR EIGENPROBLEMS WITH CIRCULAR BOUNDARIES
• Eigenfrequencies of an Elliptic Membrane
• Calculation of eigenvalues of the Helmholtz equation by an integral equation
• A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation
• Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM
• Natural mode analysis of hollow and annular elliptical cylindrical cavities
• Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply connected problem
• Numerical stability in the calculation of eigenfrequencies using integral equations

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