Theoretical analysis on Love waves in a layered structure with a piezoelectric substrate and multiple elastic layers

摘要

A method is developed to analyze the existence and behavior of piezoelectric Love waves in a multilayered structure consisting of a piezoelectric substrate and multiple elastic layers which are isotropic, nonpiezoelectric materials. The acoustic waves and electric fields in the substrate and the layers are investigated. A general dispersion equation is derived to describe the existence of Love surface waves with respect to phase velocity as a function of normalized layer thickness. An iteration formula for X_N is introduced to describe the mechanical action between the layers and the substrate at the interface. Another formula for ε_(LN), the equivalent permittivity of the wave-guide layers, is produced to describe the electric fields in the layers. The dispersion equation including a mass loading on the surface of the top layer is deduced, and a formula for calculating the mass sensitivity of the phase velocity is presented. We also find the dispersion equation with an electric shorted interface and introduce a formula for calculating the electromechanical coupling coefficient K~2. Numerical results illustrate the phase velocity, the mass sensitivity of the phase velocity and the electromechanical coupling coefficient as functions of the normalized layer thickness for the Love waves in a layered structure with a polymethylmethacrylate (PMMA) layer and a sputtered SiO_2 layer on a 90° rotated ST-cut quartz (ST-quartz) substrate.