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This paper extends the Method of Particular Solutions (MPS) to thecomputation of eigenfrequencies and eigenmodes of plates. Specificapproximation schemes are developed, with plane waves (MPS-PW) orFourier-Bessel functions (MPS-FB). This framework also requires a suitableformulation of the boundary conditions. Numerical tests, on two plates withvarious boundary conditions, demonstrate that the proposed approach providescompetitive results with standard numerical schemes such as the Finite ElementMethod, at reduced complexity, and with large flexibility in the implementationchoices.

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