Enhanced Simulation of Guided Waves and Damage Localization in Composite Strips Using the Multiresolution Finite Wavelet Domain Method

Abstract

A multiresolution finite wavelet domain method, that utilizes Daubechies wavelet and scaling functions for the hierarchical approximation of state variables, is presented. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, while additional equations of finer components are subsequently added. A coarse solution is first calculated, and finer solutions can be sequentially superimposed on the coarse solution until convergence to the final solution is achieved. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing a unique capability to separate coexisting wave modes and detect converted and reflected waves in the presence of damage. Two wavelet-based beam elements are explored, the first encompasses the Timoshenko shear beam theory and the second a high-order layerwise laminate theory for the accurate prediction of both symmetric and antisymmetric guided waves. Numerical results illustrate the inherent property of the method to a priori localize and isolate coexisting guided wave modes and their conversions, induced by different material regions and weak or debonded layer interfaces, thus demonstrating the method's intrinsic capabilities towards the design of wave-based SHM systems.