Linear piezoelectricity

This chapter presents the elements of linear piezoelectricity including mechanical and electrostatic balance laws and coupled mechanical electrical constitutive relations. The thermodynamically consistent constitutive relations are determined from a coupled electromechanical energy balance argument and expressions are given alternately considering the electric field and the electric displacement as independent fields. Appropriate electrical boundary conditions are also discussed. The theory is also specialized to poled piezoceramics. A chapter appendix provides a brief discussion of Maxwell’s equations for electromagnetics and energy transport in the quasi-static limit. A second chapter appendix discusses the properties of third order tensors.

Bending of piezoelectric beams with the flexoelectric effect under applied load at any position

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.

Evolution of electromechanical admittance of piezoelectric transducers on a Timoshenko beam from wave propagation perspective

This article analytically formulates and investigates the evolution of electromechanical admittance of piezoelectric transducers collocated on a finite beam from wave propagation perspective. First, the analytic wave solutions are obtained based on the linear piezoelectricity and the Timoshenko beam theory. Then, the evolution of wave propagation to vibration on a finite beam has been formulated in terms of a wave unit which appears periodically due to the multiple reflections at beam supports. The formulation has been extended to describe the underlying mechanism how electromechanical signatures evolve from wave units. The support conditions and material damping of a beam have been considered explicitly for both wave units and electromechanical signatures. The validity of the proposed formulation has been demonstrated through proof-of-concept numerical examples providing valuable physical insights into the relevance between wave units and electromechanical signatures.

Direct BEM for Three-Dimensional Transient Dynamic Piezoelectric Analysis

Direct boundary element method formulation for transient dynamic linear piezoelectricity is presented. Integral representations of Laplace transformed dynamic piezoelectric fundamental solutions are used. Laplace domain BEM solutions inverted in real time by the stepping method. Numerical example of transient piezoelectric analysis is presented.