Page 100 - 《应用声学》2020年第6期

第 39 卷 第 6 期 Vol. 39, No. 6
2020 年 11 月 Journal of Applied Acoustics November, 2020

⋄ 研究报告 ⋄

压电陶瓷复合换能器固有频率的有限差分法 ∗

张 超 姚春东 † 具自强 贾贺通 董子龙 武 勇

(燕山大学机械工程学院 秦皇岛 066004)
摘要：为丰富换能器固有频率的研究理论，以及提供一种新的计算方法供工程人员选择，提出了计算其固有频
率的有限差分法。以由径向极化的压电陶瓷圆管与金属预应力管沿径向复合而成的二元压电陶瓷复合换能器
为例，建立并推导了径向振动的数学模型及其有限差分形式，给出了换能器径向振动的特征方程。利用数值仿
真软件对计算实例的径向振动的固有频率进行编程计算，理论计算结果与已有实验结果符合很好，验证了有
限差分法计算压电陶瓷复合换能器固有频率的可行性及准确性。通过仿真计算，给出了换能器径向振动固有
频率与其结构尺寸的影响关系：换能器径向振动的固有频率随压电陶瓷圆管内径的增大而降低，随换能器壁
厚比的增大而降低。该文所建立的换能器径向振动固有频率的有限差分法同样适用于结构形式相近的换能器
及其他元器件。
关键词：压电陶瓷；换能器；固有频率；有限差分法
中图法分类号: O327; TB552 文献标识码: A 文章编号: 1000-310X(2020)06-0894-07
DOI: 10.11684/j.issn.1000-310X.2020.06.012

Finite difference method for natural frequency of piezoelectric ceramic
composite transducer

ZHANG Chao YAO Chundong JU Ziqiang JIA Hetong DONG Zilong WU Yong

(School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China)

Abstract: In order to enrich the research theory of the natural frequency of transducer and provide a new
calculation method for engineers to choose, a finite difference method is proposed to calculate the natural
frequency of transducer. In this paper, a two-dimensional piezoelectric ceramic composite transducer, which
is composed of a radially polarized piezoelectric ceramic circular tube and a metal prestressed tube, is taken
as an example. The mathematical model and its finite difference form of the directional vibration of the
transducer are established and derived. The characteristic equation of the radial vibration of the transducer is
given. Numerical simulation software is used to program the natural frequency of the radial vibration of the
calculation example. The theoretical calculation results are in good agreement with the existing experimental
results. The feasibility and accuracy of the finite difference method to calculate the natural frequency of
piezoelectric ceramic composite transducer are verified. The relationship between the natural frequency of
the radial vibration of the transducer and its structure size is given through the simulation calculation. The
natural frequency of the radial vibration of the transducer decreases with the increase of the inner diameter
of the piezoelectric ceramic tube, and decreases with the increase of the wall thickness ratio of the transducer.
The finite difference method for the natural frequency of radial vibration of transducers established in this
paper is also applicable to transducers and other components with similar structure.
Keywords: Piezoelectric ceramics; Transducers; Natural frequency; Finite difference method

2020-03-20 收稿; 2020-09-11 定稿
国家自然科学基金项目 (51974276)
∗
作者简介: 张超 (1995– ), 男, 山东淄博人, 硕士研究生, 研究方向: 机械系统动力学建模与仿真。
† 通信作者 E-mail: ycd04@163.com