Effect of an inhomogeneous initial stress on Love wave propagation in 0.67Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ single crystal layered structure poled along [011]_c

The propagation behavior of Love wave in 0.67Pb(Mg_1/3Nb_2/3)O–0.33PbTiO₃ (PMN–0.33PT) single crystal layered structure with the inhomogeneous initial stress varying along thickness is studied in this paper. The interface between PMN–PT layer and elastic substrate is perfectly bonded. The surface of the layered system is free of traction and electrically shorted or open. PMN–0.33PT single crystal is considered [011]_c polarized, and has macroscopic symmetry of orthogonal mm2. The Frobenius method is employed to solve governing equation with variable coefficient. The analytical dispersion equations are derived for different boundary conditions. The numerical results show that the Frobenius method can provide a good asymptotic approximation when the retained number of items in Frobenius series is sufficient. It is found that the inhomogeneous initial stress has strong effect on the dispersion characteristics comparing with constant initial stress, whereas has less effect on the cut-off frequency for the first two modes of Love wave. The gradient coefficients of inhomogeneous initial stress can obviously affect the phase velocity and corresponding electromechanical coupling factor, and can also change the distributions of mechanical displacement, electrical potential and stress. The obtained results can provide a predictable and theoretical basis for design and manufacture of high performance surface acoustic wave devices.