Excitation of shear waves in a piezoceramic medium with partially electrodized tunnel openings strengthened by a rigid stringer

An antiplane mixed boundary electroelasticity of a stationary wave process in an unbounded piezoceramic medium containing tunnel heterogeneities of opening or thin rigid inclusion (stringer) type is considered. The excitation of an electric field occurs at the expense of differences of electric potentials applied to the system of electrodes located on a free from stresses opening surface. Using the correct integral representations of the solutions, the boundary problem is reduced to the system of singular integrodifferential equations of the second type with resolvent kernels. The results of the parametric investigations characterizing the behavior of the components of an electroelastic field in the medium area and on the opening surface are given. A system of singular integrodifferential equations is obtained for investigation of a conjugated electroelastic field in a piezomedium with a tunnel along the material axis opening a rigid curvilinear inclusion, excited by a system of active electrodes, located on the opening surface. The solvable system of equations of the boundary problem is reduced to two differential equations of Helmhöltz and Laplace with respect to the amplitude of shear displacement and some auxiliary functions. The obtained system is solved numerically by a special scheme of the method of quadrature

Conditions of cracking of a stringer

In the limits of brittle failure of materials, we investigate the problem of possible cracking of an infinite stringer on the boundary of an elastic half-infinite plate. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to application of forces on the stringer. The accurate solution of a contact problem of interaction of an infinitely continuous stringer is constructed. With the help of this solution, we formulate the condition of cracking of a stringer and the necessary restrictions for external loading, which provide the contacts of a broken stringer with a plate without propagation of a crack inside the stringer. The problem considered here is of interest for theory and practice. We firstly formulate the modified problem of E. Melan and with the help of Fourier integral transformation, we construct its acoustic solution and then formulate the condition of cracking of an infinite stringer. After that, reveal the necessary restrictions on external loadings, which provide the contact of the failed stringer with a plate without propagation of the crack inside the plate