Wavelet Decompositions for High Frequency Vibrational Analyses of Plates

A wavelet-decomposed Rayleigh–Ritz model for 2D plate vibration analyses is proposed in this work. For an elastically-supported rectangular plate under Love–Kirchhoff theory, 2D Daubechies wavelet scale functions are used as the admissible functions for analyzing the flexural displacement in an extremely large frequency range. For constructing the mass and stiffness matrices of the system, the 2D wavelet connection coefficients are deduced. It is shown that by inheriting the versatility of the Rayleigh–Ritz approach and the superior fitting ability of the wavelets, the proposed method allows reaching very high frequencies. Validations are carried out in terms of both eigen-frequencies and the forced vibration responses for cases which allow analytical solutions. Effects of the wavelet parameters on the calculation accuracy and convergence are also studied.