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

TL;DR

This paper introduces a low-complexity extension of the Method of Particular Solutions for computing plate eigenmodes using Vekua approximations, demonstrating competitive accuracy and flexibility compared to standard methods.

Contribution

It develops specific approximation schemes for the MPS tailored to plates, incorporating boundary condition formulations and demonstrating efficiency and flexibility.

Findings

Competitive results with Finite Element Method

Reduced computational complexity

Flexible implementation options

Abstract

This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. 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.