The equation for the surface impedance of an inhomogeneous elastic medium in the case of periodic strips

It is demonstrated that the known nonlinear integro-differential equation for the surface impedance of an inhomogeneous elastic medium in the case of periodic structures is reduced to a system of ordinary differential equations of the first order in mechanical partial impedances. The developed impedance method is applied to a periodic system of elastic strips placed on a piezoelectric substrate. By analogy with the well-known function of surface effective permittivity the effective permittivity matrix is introduced in an explicit form to characterize the piezoelectric substrate surface loaded by elastic strips. The frequency dependence of the effective permittivity matrix is shown and the electrical admittance of a multi-electrode periodic cell is calculated.