Finite-difference modeling of piezoelectric composite transducers

Abstract

Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials J. Appl. Phys. 112, 064902 (2012) Focused high frequency needle transducer for ultrasonic imaging and trapping Appl. Phys. Lett. 101, 024105 (2012) A rigid, monolithic but still scannable cavity ring-down spectroscopy cell Rev. Sci. Instrum. 83, 043115 (2012) Acoustic resonator based on periodically poled transducers: Concept and analysisThe mechanical and electrical properties of transducers are modeled by finite-difference representations of the relevant physical equations, and the numerical problems are discussed. The theory is applied to ͑a͒ a ceramic transducer of dimensions 1 cmϫ1 cmϫ200 m, ͑b͒ a polymer P of the same dimensions, and ͑c͒ a 1-3 composite transducer consisting of transverse rods of ceramic embedded in a matrix of polymer. The results for the ceramic agree with the one-dimensional model, viz.:voltage of order 4-5 V and no resonance below 10 MHz. For the polymer, the resonant frequency of 3.9 MHz is close to the 4 MHz predicted by the one-dimensional theory. For the composite, introduction of the ceramic has an immediate effect on s 11 , s 12 and s 13 , whereas it has little effect on d 31 unless the density of the ceramic in the mix is 30% or higher.

Explicit finite-difference time-domain scheme for the simulation of 1-3 piezoelectric effect in axisymmetrical configurations

“…In the present appendix several arguments are presented in order to justify the approach introduced by equations (8) and (9). The assumption is based on the condition of constant displacement field through an axial line, and permits to obtain the physical variables in an explicit scheme.…”

“…To the best of our knowledge, the only other recent significant contributions on this topic come from Masahiro Sato et al [7,8], whose work has achieved important advances but is restricted to the two dimensional case. Other important work to be noted, in which no restrictive conditions are imposed is that of Hornsby and Das-Gupta [9].…”

Focusing of pulses in axially symmetric elastic tubes with fluid filling and piezo actuator by a finite difference simulation and a method of time reversal

“…The governing equations needed to describe a transversely isotropic piezo tube with polarization in the 3 direction are the conservation of momentum (identical to the conversation of momentum for the elastic tube), the piezo equations [7,14,15] (with the electric displacement D, the electric field E, the elastic material coefficient c ij for the piezo at constant electric field, the piezoelectric coefficient e ij and the electric permittivity coefficient b ij at constant mechanical stress) …”

Correspondence - Perfectly matched layer stability in 3-D finite-difference time-domain simulation of electroacoustic wave propagation in piezoelectric crystals with different symmetry class

“…Then, this method was adapted for simulation of elastodynamic phenomena in geophysical problems [2], [3]. In this direction, one of the main applications of the finite-difference methods has been the simulation of piezoelectric transducers in two dimensions [4] and three dimensions [5], [6]. FdTd has also been used for the simulation of electroacoustic wave propagation in piezoelectric crystals [7].…”