Low-complexity computation of plate eigenmodes with Vekua approximations\n and the Method of Particular Solutions

2013/01/05 by Gilles Chardon, Chardon, Gilles, Laurent Daudet +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Composite Structure Analysis and Optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Railway Engineering and Dynamics

paper · pdf · doi:10.48550/arxiv.1301.0908

openalex publication_date 2013/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

This paper extends the Method of Particular Solutions (MPS) to the\ncomputation of eigenfrequencies and eigenmodes of plates. Specific\napproximation schemes are developed, with plane waves (MPS-PW) or\nFourier-Bessel functions (MPS-FB). This framework also requires a suitable\nformulation of the boundary conditions. Numerical tests, on two plates with\nvarious boundary conditions, demonstrate that the proposed approach provides\ncompetitive results with standard numerical schemes such as the Finite Element\nMethod, at reduced complexity, and with large flexibility in the implementation\nchoices.\n

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