Scattering Of Sh-wave By A Circular Inclusion With Disconnected Curve And A Crack In The Piezoelectric Material Strip

Piezoelectric materials with electric-mechanical coupling effect can achieve not only the exchange of the mechanical vibration and alternating current,but also self-diagnosis and self-repair of structures,which enables piezoelectric materials to be used widely in smart structures and sensor elements,in all likelihood,piezoelectric materials tend to play an important role in design of aerospace vehicles and aircrafts in the future.Piezoelectric medium is a common new kind of intelligent material and used in production and life such as national defence and military project extensively.Structure can produce all kinds of defects caused by the natural factors and production process,such as a hole in irregular shape,inclusion with different parameters,small cracks and inclusion with a semicircular disconnected curve,these defects exist all kinds of piezoelectric elements,such as the linking section of different materials,the welding crack of piezoelectric elements,and many piezoelectric materials like plates,columns and shells,these defects make a great influence on mechanical and electrical properties,many scholars research the problems of dynamic stress of piezoelectric materials including defects such as hole,inclusion and crack and numerous valuable statistics are obtained.The piezoelectric single material strip including a circular inclusion,a circular inclusion with a semicircular disconnected curve and a linear crack,many circular inclusions with a semicircular disconnected curve and a linear crack,and the piezoelectric bi-material strip including a circular inclusion are studied by the elastic mechanics theory in the linear elastic scope respectively.The scattering of SH guided wave by a circular inclusion in the piezoelectric single material strip is studied by the complex method and repeated image superposition.The analytical expression of guided wave function and electric potential functions are obtained which satisfies the stress free condition on the upper and lower horizontal boundaries of the strip.Unknown coefficients are solved by the continuous condition of mechanical and electric field around the circular inclusion.The dynamic stress concentration factor and electric field intensity concentration factor around the inclusion are analyzed in calculating example.The dynamic stress of a circular inclusion near the linear crack in the piezoelectric single material strip under SH guided wave is analyzed.The analytical expression of guided wave function and electric potential functions are obtained.Crack and semicircular disconnected curve are established by the Green function method and “the crack-division technology”,the dynamic stress concentration factor around the inclusion and dynamic stress intensity factor at the tip of crack are given and discussed.The dynamic stress of a circular inclusion near the interface crack in the piezoelectric bi-material strip under SH guided wave is analyzed.Firstly,the bi-material media is divided into two parts along the vertical boundary,Green’s function is constructed,and a harmonic out-of-plane line source forces are applied on the vertical boundary of a strip,the analytical expression of guided wave function and related electric potential functions are solved.By the means of the repeated image superposition method,the incident wave,refracted wave and reflected wave are got which satisfy the stress free and electric insulation conditions on the upper and lower horizontal boundaries.Secondly,a pair of anti-plane forces is applied on the vertical boundary,according to boundary conditions,the first kind of Fredholm integral equations are established by “the conjunction method”.Finally,by the means of the “crack-division method”,the cracks are established,and the first kind of Fredholm integral equation is established by “the conjunction method”.The dynamic stress concentration factor aound the inclusion and dynamic stress intensity factor at the tip of crack are discussed in the calculating example.