Effect Of Circular Inclusion And Cavity On SH-Wave Scattering In A Plate

In recent years,due to the rapid progress of science and technology and the rapid development of infrastructure construction in China,the elastic wave theory is more widely used in the nondestructive testing of building structures or materials.Common building materials such as concrete,brick,stone,or the building structure composed of these building materials are usually high compressive strength and low shear strength,so the s wave occupies an important position in the structure detection.Among them,SH wave has only one out-ofplane displacement.Compared with P wave and SV wave,there is no problem of mode conversion on the boundary,so the degree of nondestructive testing based on SH wave is high.Plate material has a wide range of applications in engineering,its interior is always can be approximated as a cylindrical hole or cylinder inclusions,for example,plate inside often reserved holes to meet the routing or pipe through,or add some fiber inside the plate to increase the mechanical properties of the material.When the structure is subjected to dynamic load,SH waves will be emitted and scattered at the holes or fibers,resulting in the increase of dynamic stress concentration at the edges of the holes or fibers,which will greatly affect the strength of the material.the so-called thousand-li dike destroys the ant colony.engineering practice has also proved that the damage of the material often starts from these tiny defects.For the study of this kind of problem,the antiplane problem of the elastic plate material with holes or fibers inside can be simplified as a mechanical model of the SH-wave scattering problem of the infinite elastic strip medium with cylindrical holes or cylindrical inclusions.In this paper,the scattering of SH-waves by a cylindrical inclusion and a cylindrical cavity in the band domain is studied.In the research process,the wave function expansion method combined with complex variable function,the repeated image method,and the multi-polar coordinate translation technique are used to deduce the incident guided wave and the scattered guided wave that meet the stress free conditions of the upper and lower surfaces in the strip domain.then,the boundary stress continuity and displacement continuity conditions of the cylindrical inclusion and the boundary stress free condition of the cylindrical hole are brought in to obtain the definite solution equations.the infinite linear equations are obtained by the wave function expansion method,and the unknown coefficients are calculated by intercepting the finite terms.The main research contents of this paper are as follows:The scattering problem with two cylindrical holes in the band domain is studied in detail when the steady-state SH guided wave is incident.The influence of various factors on dynamic stress concentration coefficient is analyzed in detail.The results show that when there is only one cylindrical hole in the strip domain,the dynamic stress concentration coefficient of the hole edge will oscillate and decrease with the increase of the strip domain thickness at medium and high frequency incidence;When there are two cylindrical holes with the same size in the strip domain,the existence of no.2 hole will lead to the increase of dynamic stress concentration at the edge of no.1 hole in most cases;When the two cylindrical holes are different in size,the increase of the no.2 hole will lead to the increase of the dynamic stress concentration of the no.1 hole under the medium and high frequency incidence.In addition,the scattering of SH-waves by cylindrical inclusions and cylindrical holes in the band domain is also studied.The standing wave inside the inclusion is constructed,and by using the boundary conditions of the inclusion and the cavity,the set of definite solution equations is obtained,which is transformed into the solution of the definite solution equations.Finally,the effects of guided wave order,strip thickness,incident wave frequency,the distance between inclusion and cavity,and the size of cavity on dynamic stress concentration coefficient are analyzed.The results show that the 0-order SH guided waves,as the lowest-order one,occupy the most important position among all the SH guided waves;Compared with the "hard" inclusion,the "soft" inclusion will produce larger dynamic stress concentration;High frequency leads to the increase of dynamic stress concentration at the edge of inclusion;The influence of the distance between the hole and the inclusion on the dynamic stress concentration at the edge of the inclusion is very complicated,but the influence of the hole on the inclusion should be considered no matter how far apart.The larger the size of the hole is,the more likely it is to cause dynamic stress concentration at the edge of the inclusion.