Related Experiment Video
Updated: May 31, 2026

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
Published on: April 27, 2016
Exact second order formalism for the study of electro-acoustic properties in piezoelectric structures under an
M Lematre1, M Domenjoud, L P Tran-Huu-Hue
1LUSSI-Equipe CUP, Université François Rabelais, ERL 3106, INSERM U930, FRE CNRS 2448, ENIVL, Blois, France. mickael.lematre@univ-tours.fr
Abstract:
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%).
Related Concept Videos
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Second Order systems II
If ζ...
Hooke's Law
Second-Order Circuits
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Residual Stresses in Bending
Sound as Pressure Waves
The pressure fluctuation depends on the difference in displacements between the successive points in the...
