Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon-Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.
Demo : ir_interpolation.zip (Matlab/Octave code).
Compares the proposed method with irregular and regular sampling, and low-pass interpolation with regular sampling.
Chardon, A. Leblanc, L. Daudet, Plate impulse response spatial interpolation with sub-Nyquist sampling, Journal of Sound and Vibration, Volume 330, Issue 23, 2011, pages 5678-5689, doi:10.1016/j.jsv.2011.07.003, [.bib][pdf]