| In general,it is difficult to avoid all kinds of defects,such as cavities and inclusions,when producing the plate and strip used in the engineering project.The mechanical properties of materials with defects will be significantly affected by external load.Under the action of external force,due to the geometric discontinuity of materials,a relatively serious stress concentration phenomenon will occur around the defects,which will adversely affect the safety of the project.Therefore,it is of great significance to study the phenomenon of dynamic stress concentration around defects.In addition,piezoelectric materials have gradually begun to be widely used in engineering project.Piezoelectric materials can realize the mutual conversion of mechanical vibration and alternating current,which makes piezoelectric materials widely used in intelligent structures and sensor elements.Therefore,piezoelectric materials will play an important role in the design of future aerospace vehicles.Piezoelectric medium is a common new intelligent material,which has great application value in national defense,military industry,mechanical design and so on.Because of the piezoelectric sensitivity,defects not only affect the mechanical properties of piezoelectric media,but also affect its electrical properties significantly.Based on the linear elastic theory,the scattering of SH guided waves in single-phase piezoelectric media with the circular cavity and two-phase piezoelectric media with the circular cavity are firstly analyzed.Then on the basis of analytical methods,pioneering solved using the finite element method(FEM)analysis containing complex cavities or inclusions strip elastic medium of SH wave scattering problems.This paper makes up the deficiency of previous studies and the finite element method is used to solve the scattering of SH waves by non-circular cavities and inclusions,infinite number of cavities and inclusions in the strip.The main work involved in this paper can be summarized into the following four parts:(1)In the first part,the scattering problem of SH guided waves in single-phase strip piezoelectric media with the circular cavity is studied.The expression of SH conduction wave and its excitation potential function satisfying the horizontal boundary stress free and electrical insulation conditions is derived by using the method of repeated image superposition.Given the incident guided wave,the integral equations for solving the problem were established by using the stress free boundary condition around the circular cavity.Then,the analytical expressions of the dynamic stress concentration factor(DSCF)and the electric field intensity factor(EFICF)around the circular cavity were obtained.The effects of incident wave frequency,medium parameters and round cavity location on DSCF and EFICF are analyzed by numerical examples.(2)In the second part,the scattering problem of SH guided waves in bi-phase piezoelectric strip media with the circular cavity is studied.First,the two-phase piezoelectric strip medium is divided into two parts along the vertical boundary,and the Green's function is constructed.Assume a source load of a plane line at any position on the vertical boundary,and solve the unknown factor by using the continuity condition around the circular cavity.Then the expressions of displacement function and potential in piezoelectric medium under line source load are obtained.When the guided SH wave is horizontally incident into the stripshaped medium,various wave functions in the strip-shaped medium meet the conditions of free stress and electrical insulation on the horizontal boundary,and the expression of the wave function is constructed by the method of repeated mirror-image.Finally,the integral equations are processed and solved by applying the unknown plane external forces and the internal and external electric fields on the vertical boundary of the partition plane.The electric field intensity concentration factor and the stress intensity concentration factor near the boundary of the circular cavity in the biphasic piezoelectric medium are studied.(3)In the third part,the scattering problem of SH guided waves in elastic strip-shaped media with complex types of cavities is studied.Firstly,SH guided waves satisfying free horizontal boundary stresses in the strip are derived by using the method of repeated image superposition.Given the incident guided wave,the integral equations for solving the problem were established by using the stress free boundary condition around the circular cavity,and the analytical expressions of the DSCF and the EFICF were obtained.Then,COMSOL software is used to simulate the scattering problem of SH waves in elastic media with cavities,and the finite element results which are consistent with the analytical results are obtained.After verifying the correctness and accuracy of the finite element method,the number of cavities,the shape of cavities and the boundary shape of the strip are directly changed in the finite element software to obtain the distribution diagram of dynamic stress concentration around the cavities in various complex situations which were difficult solved by using the analytical method.(4)In the fourth part,the scattering problem of SH guided waves in elastic strip-shaped media containing complex types of inclusions is studied.Firstly,SH guided waves satisfying free horizontal boundary stresses in the strip are derived by using the method of repeated image superposition.The unknown factor in the scattering wave expression is solved by using the continuity condition of the boundary of the circular inclusion,and then the stress intensity concentration factor near the boundary of the circular inclusion is analyzed.Then,COMSOL software is used to simulate the scattering of SH waves in elastic strip-like media with circular inclusions,and the finite element results which are consistent with the analytical results are obtained.After verifying the correctness and accuracy of the finite element method,the finite element software can directly change the number of inclusions or add the media with different elastic parameters(such as welding seam)in the strip to obtain the distribution diagram of dynamic stress concentration around the cavity of various complex situations that were difficult solved by using the analytical method. |
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