The objective of this study is to model the propagation of guided waves in piezoelectric structures subjected to a prestress gradient. The constitutive equations for a piezoelectric bulk material are first modified to take into account a uniform prestress on a given cross section. Then, these modified constitutive equations are used to derive a formalism for the propagation of guided waves in piezoelectric structures under a prestress gradient. In particular, we modify the recursive stiffness matrix method to introduce a gradient of stress in a piezoelectric structure. Numerical studies are then led for a bending and for an exponential stress profile. For a piezoelectric plate, the Lamb and shear horizontal modes are found to be sensitive to the prestress gradient. In particular, some key features of dispersion curves appearing in the presence of a gradient of properties are highlighted. In the last part, these results are extended to a piezoelectric film laid down on a substrate in order to model the importance of the stress gradient on the behavior of an integrated structure. Lithium niobate is used for the plate and film material, and a silicon crystal is used as the substrate.
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