A comparison of numerical and semi-analytical proper orthogonal decomposition methods for a fluttering plate

Both a simple POD (S-POD) method calculating derivatives of the POD modes (POMs) numerically and a semi-analytical POD (P-POD) method with a projection from the POMs to the Rayleigh-Ritz modes are used to investigate a supersonic fluttering cantilever plate. Numerical simulations demonstrate that the S-POD method avoids the complex mathematical derivations due to the mode projection in the P-POD method, and the computational cost is remarkably reduced. In particular, the S-POD method is approximately 50 times faster than the P-POD method. In addition, the simply supported plate is briefly discussed using the P-POD method, which is much more efficient compared with the Galerkin method, especially for the panel with large a/b. The present study will give the researchers crucial suggestions on how to choose the S-POD method or the P-POD method for the panel with different length-to-width ratios or support conditions.