Scattering Of SH Waves By Depressions And Cylinders In Elastic Strip

Since China is located between the two major earthquake zones in the world,it has been suffering from the erosion of earthquake disasters since ancient times.The property damage and casualties caused by the earthquake are numerous.Most of the materials damaged by earthquake are rock and soil,rock on the earth’s surface,or commonly used building materials in civil engineering.These materials or structures have high compressive strength but poor shear resistance.As a kind of shear component of seismic wave,SH wave has been paid enough attention by researchers in the past.Plate materials and structures are widely used in civil engineering.In engineering practical,people often reserve cylindrical concave channels on the plate surface to meet the requirements of line or drainage.When the SH wave propagates in these materials or structures,it will scatter in the depression and cause the increase of dynamic stress concentration and displacement amplitude.In addition,the ultrasonic SH guided waves have great advantages in the defect detection of plates because of its simple dispersion characteristics Therefore,it is of great scientific significance and engineering value to study the propagation characteristics of SH wave in plate.For the above problems,the plate materials and structures whose length and width are much larger than the thickness can be approximately studied according to the strip shape domain.At present,most of the literatures have studied the scattering of SH wave in the medium of full space and half space.Only a few literatures have studied the SH-wave scattering by internal defects of the strip.In this paper,the scattering problem of the depression and the cylinder in the elastic strip medium subjected to SH wave is studied.In this paper,the wave function expansion method and the multiple image method are used to derived the expression of the SH waves in the strip domain.And the boundary conditions are used to obtain the definite solution equation.Then,we use the Fourier expansion method to get infinite linear equations.And the solution of the problem is obtained by truncating the equations.Finally,the dynamic stress concentration and displacement amplitude are discussed by numerical results.The research contents and results of this paper include:The scattering problem of multiple semi cylindrical depressions on the boundary of strip domain under for incident steady-SH guided waves is studied。 The analytical solution is given.By using the multiple image method,the scattering wave expression satisfying the free stress conditions of the upper and lower straight boundaries of the strip domain is constructed.The accuracy of the method is discussed by numerical examples.And the dynamic stress concentration around the depression and the displacement amplitude of the upper and lower boundaries of the depression are analyzed.The results show that when there is only one depression,the middle and high frequency incident wave and the small thickness elastic strip will cause higher dynamic stress concentration on the edge of the depression,and the maximum value of the displacement amplitude of the upper boundary will appear near the incident side of the depression;when there are two depressions,no matter how far apart the two depressions are,the influence between them cannot be ignored.The scattering characteristics of SH guided waves in strip with a half cylindrical depression and a cylindrical inclusion are studied.First,the theoretical derivation is carried out,and the SH wave in the strip domain is constructed by using the guided wave expansion method.Then the numerical solution is obtained by solving the truncated infinite equations.Finally,the influences of the order of guided waves,the parameters of the inclusion and the distance between the depression and the inclusion on the dynamic stress concentration and the displacement amplitude are analyzed.The results show that the dynamic stress concentration coefficient caused by the 0-order guided wave in the propagating SH wave is larger;the "hard" inclusion can reduce the dynamic stress concentration along the edge of the inclusion;the influence of the distance between the depression and the inclusion on the dynamic stress concentration is complex.The magnitude of displacement amplitude and the frequency of oscillation decrease after the steady-state SH guided wave passes through the inclusion.Therefore,the detection of inclusion or depression in the strip domain can be realized by appropriately selecting the order and frequency of the incident guided wave.