The Scattering Of SH-wave By Cylindrical Debonding Lining And Crack In Interface

There are a variety of defects that the physical properties are discrete in natural mediumand engineering composite materials, such as inclusions, holes, linings, cracks, etc. It willsurely generate elastic waves in its interior when these natural medium and engineeringcomposite materials are subjected to dynamic loads. These elastic waves will generatescattering waves when elastic waves encounter defects in process of propagation. The inverseproblem of elastic wave scattering (analysis of inter-relationship between scattering wavesand the geometry, orientation, size and physical properties of defects, or analysis of reversingthe position, size of scattering body, the physical properties of surrounding medium and theinformation of reflected source on the premise that scattering effects of elastic wave aredetected in the test) is great significance to the problems of elastic wave scattering by thedefects of elastic medium in engineering domain such as mineral and oil exploration,non-destructive detecting of fixed quantity, radar, water sonar and blasting, ect.Based on the theory of complex functions and Green’s function, this thesis studies theproblem of SH waves scattering which is caused by a interface semicircular debonded elasticlining and a interface semicircular debonded elastic lining with interface crack in whole space.Firstly, a Green’s function of elastic half space including semi-circular lining hill isconstructed, which is an essential solution to the displacement field of an out-of-planeharmonic line source loading on the horizontal surface at any point. Secondly, by“conjunction” method, it conjoins the two domains of an elastic half space with thesemi-circular canyon in upper top and an elastic half space with semi-circular lining hill inbottom half around the shared “conjunction” boundary，which meets the condition ofcontinuity of stress and displacement，and constructs the solution of displacement function tothe problem of SH waves scattering, which is caused by interface semicircular debondedelastic lining. Finally, by the method of crack division, the crack is formed. reverse stressesare inflicted along the crack, that is out-of-plane harmonic line source loading, which areequal in the quantity but opposite in the direction to the stresses produced for the reason ofout-of-plane line source loading scattering by circular lining structure, are loaded at the regionwhere crack will appear, the crack can be make out. Then, the expressions of displacementand stresses are established while interface semicircular debonded elastic lining and crackexist simultaneously. The work in detail is as follows:1. The problem of scattering of SH waves excitated by semi-circular lining hill while bearing out-of-plane harmonic line source load on horizontal interface is investigated. Firstly,the displacement function of incidence wave by a out-of-plane harmonic line source load onarbitrary point of horizontal interface is given. Secondly, it divides the solution domain intotwo domains, the one is an elastic half space with the semi-circular canyon, and the secondone is a cylindrical lining; it constructs the scattering wave of semi-circular canyon meetingthe stress free boundary condition on the horizontal interface and the standing wave ofcylindrical lining satisfying the stress free boundary condition on the semi-circular hill; then,it conjoins the two domains to meet the condition of continuity of displacement and stressaround the common “conjunction” boundary and the stress free boundary condition of circularlining inside boundary, and a series of infinite algebraic equations can be obtained to settlethis problem. In the end, the properties of Green’s function and the numerical expressions ofthe ground motion in the horizontal surface are discussed.2.The problem of scattering of SH wave by interface semicircular debonded elasticlining of two-phase mediums is studied. Firstly, it divided the whole model into the upper halfelastic space with the semi-circular canyon and lower half elastic space with semi-circularlining hill. In lower half space, Green’s function constructed in forth part of this paper is used,upper half part and lower half part are conjoined by method of “conjunction”, andsemicircular debonded elastic lining is constructed by meeting the condition of continuity ofdisplacement and stress on interface when upper half part and lower half part are conjoined,and the expressions of stresses and displacement is given. Finally, as an example, it conductsthe results of dynamic stress concentration factor and analyzes the influences by thedifference parameters of mediators on the incident wave. As an example, the displacementmode of scattered wave at far field and scattering cross-section are given, and the influenceson the far field solution by different parameters are discussed.3.The problem of scattering of SH wave by a interface semicircular debonded elasticlining of two-phase mediums and interface linear cracks originating at edge of lining isinvestigated. We divided the whole model into upper elastic half space with the semi-circularcanyon and lower elastic half space with semi-circular lining hill. In lower half space.Semicircular debonded elastic lining is constructed by meeting the condition of the continuityof displacement and stress on interface when upper half part and lower half part are conjoined,and linear cracks is constructed by the method of crack incision, upper half part and lowerhalf part are conjoined by method of “conjunction”. In the end, some examples and results ofdynamic stress intensify factor are analyzed.4. The problem of scattering of SH wave by a interface semicircular debonded elastic lining of two-phase mediums and linear cracks originating at arbitrary position of interface isinvestigated. In this problem, the linear cracks and the debonded elastic lining is notconnected. The method of constructing Green’s function is the same as the method of forthproblem. The subject is inverted into the solution of the dynamic stress intensity Ⅲ mode ofthe interface cracks. And some results of dynamic stress intensify factor are discussed.