A Numerical Method For Mode Separation Of Ultrasonic Guided Waves In Pipe And Plate Structures

Ultrasonic guided waves have great potential in nondestructive testing for various engineering structures.However,due to the dispersive and multi-mode nature of guided waves,the properties of guided waves are much more complex than body waves.Usually,the dispersion curves are necessary for studying of propagation properties of guided waves.Traditionally,one has to plot all the points that satisfy dispersion equations one by one in the frequency-wavenumber domain or frequencyvelocity domain.This kind of dispersion curve charts does not give an automatic separation between different modes;instead,one need to distinguish them by experiences.Accordingly,all the scattered points on dispersion curves are also saved together in a big matrix,which brings difficulty for further studies.To tackle with the problem,this paper proposes an automatic mode separating and tracing algorithm in plotting dispersion curves,which works in both real and complex wavenumber domains.This method searches all the modes from high to low frequency points.Firstly,the wave numbers of each mode are obtained by the modulus convergence method at the highest and second highest frequencies.Then,according to the gradient,the wave number at the next frequency point is estimated,and converges to the exact value by iterative root-searching process in a nearby subspace.This process is repeated until the cut-off frequencies are reached.When two or more modes are approaching closely,the displacement distribution of each mode is drawn and the Pearson correlation coefficient is introduced to judge the direction for each mode at the next frequency point.This proposed mode tracing algorithm can also be applied to the complex domain.When the dispersion curve reaches the cut-off frequency in real wavenumber domain,we then extend the rootsearching subspace into the complex domain according to the characteristics of the dispersion curve A two-dimensional spatial modulus convergence root-finding method based on genetic algorithm is proposed.By using this method,a complete spatial dispersion curve can be traced.In this paper,the dispersion characteristics of guided waves in several typical structures are verified.Firstly,the dilatation wave in thin-walled cylindrical pipes and the classical Lamb wave in single-layer plate are calculated.The results show that the calculation results agree well with theoretical values,and mode separation is also successful.Then,the dispersion equation of generalized Lamb guided waves in multilayer anisotropic plates is derived by global matrix method.The modal separation and searching are carried out using the method proposed by the paper.The calculated results are in good agreement with the scatter plots of previous work,however,the curves are plotted separately,the data are stored separately for each mode.This method provides a refined algorithm for theoretical and numerical analysis of ultrasonic guided waves,which can effectively reduce computational cost and optimize data formation.The calculation results of this method can provide theoretical basis and data reference for further studies of non-destructive testing of ultrasonic guided waves.