★ Actual plane wave velocities differ from about 4% with the natural ones. ★ Crosses appear between curves of actual quasi-shear velocity with the pre-stress. ★ Coupling coefficient Kt is almost unchanged between the two coordinate systems. ★ Electrical input admittance differ from few percents between both formalisms. ★ Difference of pulse-echo responses can be compensated with quarter wavelengths.
In this study we develop the exact second order formalism of piezoelectric structures under an external mechanical stress. Indeed, previous models are approximated since they consist in deriving all the equations in the natural coordinate system (corresponding to the pre-stress free case). Hence, our exact formalism proposes to obtain the whole of equations in the current coordinate system (which is the coordinate system after the pre-deformation). Then, this exact formalism is used to derive the modified Christoffel equations and the modified KLM model. Finally, we quantify the correction with the approximate formalism on several transfer functions and electro-mechanical parameters for a non hysteretic material (lithium niobate). In conclusion, we show that for this material, significant corrections are obtained when studying the plane wave velocities and the electrical input impedance (about 4%), whereas other parameters such as coupling coefficient and impulse response are less influenced by the choice of coordinate systems (corrections less than 0.5%).