Functionally Graded Viscoelastic Artificial Boundary Layer And Its Application In Time Domain Analysis Of Wave Problems

Elastic waves possess numerous advantages such as strong penetration capability,long propagation distance and energy concentration when they propagate in various structures,which make them extensively applied in diverse fields like non-destructive testing,geological exploration,earthquake resistance and seismic response,radar and medical equipment.Utilizing the propagation characteristic of elastic waves in different media to detect structural performance is of paramount importance in addressing engineering issues.However,the utilization of analytical methods to resolve the elastic wave propagation problems in different structures becomes increasingly challenging because different types of structures are equipped with different boundaries.Hence,numerical methods are developed to investigate the propagation of elastic waves in diverse complicated structures.In the numerical simulation process,setting reasonable artificial boundaries can greatly reduce computational costs without sacrificing accuracy.This paper primarily concentrates on artificial boundary and relevant problem simulation in numerical simulation of wave problems.The main research contents of this article include:(1)The concept of functionally graded viscoelastic artificial boundary layer is introduced when the size of the research object is much larger than the elastic wave length and the surface features of the structure.To investigate the propagation characteristics of longitudinal waves in a one-dimensional rod consisting of elastic and functionally graded viscoelastic materials,the WKB method is used to find the analytical solution for longitudinal wave propagation in functionally graded viscoelastic materials.By applying the continuity of displacement and stress at the interface between elastic material and functionally graded elastic material,the viscosity change function that complies with complete transmission and no reflection of the functionally graded viscoelastic material is established.Moreover,the conditions zero reflection and complete attenuation of the functionally graded viscoelastic artificial boundary layer are ascertained.(2)Based on the analytical condition of non-reflection and complete attenuation at the interface between functionally graded viscoelastic materials and elastic materials,this study provides two setting methods the functionally graded viscoelastic artificial boundary layer and the gradient viscoelastic change function for the finite element numerical simulation process.The functional gradient viscoelastic artificial boundary layer with sub layer thickness of 0.2λ and viscosity change of k=2 in 1D structures,and sub layer thickness of 0.3λ and viscosity change of k=2 in 2D structures have demonstrated excellent absorption performance on elastic waves.Additionally,a composite artificial boundary layer with a low reflection boundary added outside the functional gradient viscoelastic artificial boundary layer is proposed,which exhibits better absorption performance according to the numerical simulation results.(3)The functionally graded viscoelastic boundary layer is employed as the artificial boundary for numerical simulation to examine the propagation of Lamb waves in defect-free plates vs.plates with defects.Numerical calculations reproduce the dispersion of Lamb wave propagation in the time domain.By analyzing the characteristics of Lamb wave propagation in thin plates containing defects of different shapes and sizes,it is discovered that when the defect size is the same but the shape is different,the square defect reduces the displacement amplitude of S0 mode the most conspicuously.When the shapes of the defects are identical but the sizes differ,the displacement amplitudes of both A0 mode and S0 mode decrease correspondingly.The displacement curves of both A0 mode and S0 mode manifest hysteresis in which the hysteresis time is proportional to the size of the defect.According to the research findings,the functionally graded viscoelastic artificial boundary layer is an effective approach in tackling numerical simulation of wave problems.By combining this layer with the low reflection boundary layer,a better non-reflection effect can be achieved.The conclusions drawn from this study can offer a new artificial boundary setting technique for numerical analysis of wave problems.