基于FDTD的压电换能器模型

The Modeling of Piezoelectric Transducers Using the FDTD Method

提出了基于时域有限差分法(FDTD)对一维压电换能器的机电耦合现象进行数值分析的新方法。利用时域有限差分法理论对压电材料的控制方程、牛顿方程在空间和时间上进行了心差分离散化,并首次提出了压电换能器的收发电压信号和压电控制方程间关系的迭代差分方程,借助这些差分方程,从而能直接给出压电换能器声场传播的时域信息。利用此法分析了压电换能器匹配层厚度对接受电压波形的影响,并得到了其质点速度和质点应力传播的时空分布图。另外,还提出了利用Prony法替代FFT法,从而利用更短时域响应来得到压电换能器的频域特性。仿真结果表明,提出的模型能有效分析多层压电换能器的稳态和瞬态激励响应的传播特性。

The finite-difference time-domain （FDTD） method is extended to analyze one-dimensional multilayer transducers. In this method, the piezoelectric governing equations and Newton＇s equation are discretized to centered finite-differences, and the update equations for the transmit-receiver voltage and the piezoelectric governing equations are derived for the first time, then numerical solutions of the acoustic propagation in the time domain can be obtained by these difference equations. The model is applied to analyze the influence of thickness of the matching layer on the receiver voltages, and the propagation of particle velocity and the particle stress signals are demonstrated in space-time. In addition, this letter also proposed Prony＇s method as an alternative to FFT since it capable of obtaining resonant frequencies from shorter time-domain responses. The technique is shown to be effective for the analyse characteristics of the wave propagating in multilayer transducers for both transient and steady-state problems.