Time-harmonic Lambʹs problem for a system comprising a piezoelectric layer and piezoelectric half-plane

The time-harmonic Lamb problem is considered for the system consisting of a piezoelectric covering layer and piezoelectric half-plane. The investigations are carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity. The plane-strain state is considered and it is assumed that between the covering layer and half-plane perfect contact conditions are satisfied. The boundary value problems under consideration are solved by employing Fourier exponential transformation techniques with respect to coordinates directed along the interface line. An algorithm is proposed and employed to obtain numerical results on the distribution of the normal and shear stresses acting on the interface plane. Moreover, numerical results on the distribution of the electric potential in the covering layer are also presented and discussed. The piezoelectric materials PZT-5A, PZT-5H, PZT-4 and PZT-7A are examined. In particular, it is established that the piezoelectricity of the covering layer material (half-plane material) causes to decrease (increase) the absolute values of the aforementioned stresses acting on the interface plane.