Study On Propagation Characteristics Of Ultrasonic Guided Waves Via Semi-analytical Wavelet Finite Element Method

With the rapid development of high-end equipment manufacturing,the automation,lightweight and high efficiency of modern mechanical structure design has put forward higher requirements for the safety and reliability of new structures and materials.However,the certain mechanical structures have long served in harsh conditions such as remote areas,low temperatures,high pressures,and are also needed to withstand stress loads and fatigue loads in different directions,inevitably resulting in degradation of structural performance and deriving different degrees of damage,and even huge economic losses and casualties.Therefore,it is of great scientific and theoretical significance and engineering application value to effectively monitor the health of key structures in a timely manner,ensure the safety of equipment structures,avoid economic and property losses and major disasters.Compared with traditional nondestructive testing techniques,the ultrasonic guided waves have the advantages of long propagation distance,low energy attenuation,and sensitivity to both internal and external defects in the waveguide medium.This is why ultrasonic waveguide based detection technology has become a research hotspot in the field of non-destructive testing and structural health monitoring.A detailed understanding of the propagation mechanism of the ultrasonic guided waves is a prerequisite and foundation for the accurate identification and localization of structural defects.As guided waves are high frequency waves,the analysis of propagation characteristics is influenced by the "short wave problem" and the " pollution error effect",which means that the mesh discretization needs to be sufficiently fine.Also,the high resolution of the dispersion curves and wave structure vibrations requires the eigenvalue problem to be solved iteratively at multiple frequencies,which will inevitably increase the size of the solution of the system matrix,leading to more stringent computational efficiency and computer configuration requirements.Using traditional methods to solve the propagation characteristics of guided waves in complex and large cross-section structures has disadvantages such as insufficient computational accuracy,low efficiency,and unstable convergence.Therefore,in view of the above problems,the exploration of efficient analysis methods for the propagation characteristics of guided waves has become an urgent task in the research of guided wave based structural health monitoring technology.In order to solve the above problems,the semi-analytical wavelet finite element method is proposed in this paper for analyzing the propagation characteristics of guided waves.At first,the B-spline wavelet on the interval(BSWI)scale functions with good tight branching,smoothness and symmetry on a finite interval,and with displaying analytical expressions is used as the interpolation function,the BSWI element with high accuracy and efficiency is constructed.The cross section of the waveguide medium is discretized by constructed wavelet elements,assuming that the waveguide propagates with simple harmonic vibrations in the direction of propagation and establishing a semi-analytical wavelet finite element model for analyzing the propagation characteristics of ultrasonic guided waves,thereby completing efficient and accurate analysis of guided wave propagation characteristics.The proposed method realizes the application of wavelet numerical methods in the analysis of guided wave propagation characteristics and provides a theoretical basis and calculation method for the subsequent analysis of propagation characteristics in plate structures and special-shaped structures.In view of the problems of low accuracy,low efficiency,and unstable convergence in traditional methods for solving propagation characteristics problems,the numerical results of the analytical method and the semi-analytical finite element method are introduced into numerical examples of plate structures and special-shaped structures as a comparison,verifying that the proposed semi-analytical wavelet finite element method has the advantages with high accuracy,excellent efficiency,and stable convergence.The conversion of the acquired array signals from the time-space domain to the frequency-wave number domain in simulations and experiments using the two-dimensional Fourier transform technique,and the transformation results are compared with the theoretical results obtained by the semi analytical wavelet finite element method.The simulation and experimental results show that this method can effectively improve the computational efficiency while ensuring accuracy,and can save about 90% of the solution time in the propagation characteristics analysis of waveguide structures,thus verifying the superiority of the method.Based on the above research,an ultrasonic guided wave propagation characterization system was designed and developed based on the MATLAB App Designer graphical user interface platform.The proposed semi-analytic wavelet finite element method is summarized and demonstrated,and practical engineering applications of the method are realized.