The Application Of The Method Fundamental Of Solutions To Calculate Ultrasonic Guided Wave Scattering Problem

As a non-destructive testing method for large-scale plates and pipes,ultrasonic non-destructive testing is attracting increasing attention of researchers.Traditional ultrasonic detection techniques using body waves are time-consuming because they require a comprehensive inspection of the structure.Ultrasonic guided wave detection can overcome this problem and it has the advantages of long propagation distance,wide range,fast speed and strong anti-interference ability.To take full advantage of ultrasonic guided waves,we need a thorough understanding of its scattering properties.In this paper,a numerical method combining the modified boundary element method and the method of fundamental solutions is proposed to solve the scattering problem of ultrasonic guided waves.To solve the scattering problem of a single cavity in waveguide structure,there are mainly the following two steps.First,the modified boundary element method with far-field displacement model is introduced.For the complete model without cavity,the boundary element method is applied to discretize the boundary of the model.In order to eliminate the false reflection wave caused by the model truncation,the far-field displacement hypothesis is introduced.At the same time,the integral on the infinite boundary is transformed into the integral on the known finite boundary by using the reciprocity theorem in the elastic dynamics,which is incorporated into the boundary integral equation as a modification term.Second,the method of fundamental solutions is used to simulate the scattered wave field.The scattering wave field caused by the cavity is approximated to the superposition of a series of virtual point sources radiation wave fields.In order to avoid singularity,these virtual point sources are placed inside the cavity,and their strength is determined by the boundary conditions of the cavity.Finally,the above two parts are combined into a whole matrix,and the near-field displacement field,far-field scattering coefficient of each guided wave mode and the strength of virtual point sources can be solved simultaneously.The scattering fields of SH guided wave and Love wave are solved and the convergence is checked.Besides,the results of the previous numerical methods are compared and the results are accurate.This method only needs to model once,and the modeling speed is fast.It has a great advantage in model updating when solving the forward and inverse problems in the future.Finally,using the scattering coefficient obtained from the forward problem,the inverse problem is explored and a better quantitative reconstruction result is obtained.