Surface SH-waves in pre-stressed piezoelectrics with functionally graded

A model of a ferroelectric structure consisting of a homogeneous piezoactive half-space with an inhomogeneous coating which is either a layer or a packet of homogeneous or functionally graded piezoactive layers is suggested. It is assumed that the half-space, as well as the coating, being piezoelectrics of the hexagonal syngony of a 6 mm class in their intrinsic state, are in the conditions of the action of the initial mechanical stresses. Investigations of dynamic properties of the functionally oriented pre-stressed structures are carried out in Lagrangian rectangular coordinate system. Linearized constitutive relations and motion equations are used. The boundary problem for the system of differential equations in partial derivatives is reduced to the system of ordinary differential equations by means of the operational calculus. In case of the structure homogeneous components, Green’s function is constructed analytically in a closed form on the basis of solving the system of differential equations with constant coefficients. In case of inhomogeneous (functionally graded) components, the system of differential equations with variable coefficients is reduced to the system of Cauchy initial problems by means of a special substitution. In this case, Green’s function is constructed numerically on using Runge-Kutta numerical methods with Merson modification, which allows us to control the error of calculations in an effective way. When constructing Green’s function of the ferroelectric structure with an inhomogeneous coating, we used the matrix approach that allows us to combine analytical and numerical methods of constructing its isolated components. The influence of the type and the value of the initial stresses on the peculiarities of the surface wave propagation in heterostructures is studied. It became possible to determine the conditions under which the action of the initial mechanical stresses leads to the increase of Bleustein-Gulyaev wave velocity with respect to the velocity of the original material, as well as the conditions under which the piezoelectric structure ceases to be a weakly inhomogeneous one.