Numerical modeling of flexural wave propagation for damage quantification using Hermite radial point interpolation method based on Gaussian RBF

A variety of numerical methods were developed for the wave propagation analysis in the field of structural health monitoring. In this framework, meshless methods are suitable procedure for the analysis of problems such as damage initiation and its propagation or the fracture of materials. In this study, Hermit-type radial point interpolation method (HRPIM) is investigated for the numerical modeling of flexural wave propagation and damage quantification in Euler-Bernoulli beams using MATLAB. This method employs radial basis function (RBF) and its derivatives for interpolation which leads to Hermitian formulation. The evaluation of performance and capability of HRPIM is based on the comparison between the captured HRPIM ang benchmark signals using the root mean square error (RMSE) and reflection ratio from damage. The algorithm of damage quantification is the analytical solution which relates the reflection ratio to the damage extent. In this study, Gausian-type RBF is utilized and the number of field nodes, the size of support domain, shape parameters of RBF, the number of polynomials in the interpolation formula, the arrangement of background cells and the number of Gaussian points in damage length are the effective parameters on results. Based on the evaluation, the acceptable values and range of theses parameters are presented for correct modeling.