Multiresolution finite wavelet domain method for efficient modeling of guided waves in composite beams

Abstract

A Multiresolution finite wavelet domain meshless approach is presented for the simulation of guided waves in composite beams. The Daubechies wavelet and scaling functions are both employed as basis functions and their remarkable properties for the hierarchical spatial approximation of state variables are explored. The first level of the multiresolution approximation provides the coarse solution, while finer resolution components are sequentially calculated and superimposed on the coarse solution, until the desired level of accuracy is achieved. The development of the multiresolution wavelet-based beam element that encompasses first-order shear deformation theory kinematic assumptions is described, and the multiresolution equations of motion including stiffness and mass matrices are formulated. Numerical results for the simulation of guided wave propagation in aluminum and laminated composite beams are presented, demonstrating substantial reduction in computational effort compared to single resolution approaches and traditional finite elements. Convergence studies using various Daubechies wavelet interpolation functions, are evincing extraordinary convergence rates with very low requirements of grid points per wavelength. Furthermore, additional benefits of the proposed method are encompassed in the analysis of multiple guided wave modes, attributed to the low-pass filter behavior of the scaling functions and the band-pass filter behavior of the wavelet functions that can result in isolation of different wave modes by the individual resolution components of the total solution.