Page 89 - 201805

第 37 卷 第 5 期 Vol. 37, No.5
2018 年 9 月 Journal of Applied Acoustics September, 2018

纪念应崇福院士诞辰100周年

无障板圆形活塞换能器的辐射阻抗 ∗

莫喜平 †

(中国科学院声学研究所 北京 100190)

摘要 辐射阻抗是换能器的最重要辐射声场特性参数之一，影响着换能器的谐振频率、频带宽度、效率以及辐
射声功率等。经典声学理论用一阶贝塞尔函数和斯特鲁夫函数给出了圆形活塞换能器辐射阻抗的数学表达
式，但仅适用于无限大障板条件。该文用 ANSYS 有限元软件计算了无障板圆形活塞换能器的辐射阻抗，给出
了数值解结果，通过与无限大障板条件下的理论结果相比较，显示了二者之间的偏离情况，尤其是在低频时差
异显著。为了借助 MATLAB 工具模拟无障板圆形活塞换能器的辐射阻抗，并给出较准确的数学表达，选择了
一系列初等函数以及它们的复合函数进行曲线拟合，最终给出了辐射阻和辐射抗关于 ka 的函数表达式，在 ka
值从 0.08 到 20 范围内与有限元计算结果很好吻合。
关键词 辐射阻抗，无障板活塞，曲线拟合，数学表达式
中图法分类号: TB565 文献标识码: A 文章编号: 1000-310X(2018)05-0671-04
DOI: 10.11684/j.issn.1000-310X.2018.05.010

Radiation impedance of the unbaffled circular piston transducer

MO Xiping

(Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)

Abstract The radiation impedance is one of the most important characteristics of the acoustic field of a
transducer, because it affects the resonance frequency, bandwidth, efficiency and power of the transducer.
The mathematical expression of radiation impedance of circular piston by using first-order Bessel and Struve
functions only for that in an infinite baffle was given in classic acoustics theory. In this paper the radiation
impedance of an unbaffled circular piston has been calculated by FEM software (ANSYS), the numerical results
have been given, and compared with the theory results of circular piston in an infinite baffle. It is discovered,
the radiation impedance of an unbaffled piston is distinct from that in an infinite baffle, especially at low
frequency. To simulate the radiation impedance of an unbaffled circular piston with MATLAB software and
obtain an exacter mathematical expression, selected a series of elementary function and their composite function
for curve fitting. Radiation resistance and reactance as explicit function of ka have been provided, that is in
good agreement with calculated by FEM in the range of ka from 0.08 to 20.
Key words Radiation impedance, Unbaffled piston, Curve fitting, Mathematical expression

2018-06-11 收稿; 2018-08-25 定稿
∗ 中国科学院声学研究所率先计划项目
作者简介: 莫喜平 (1966- ), 男, 辽宁人, 研究员, 博士生导师, 研究方向: 水声换能器。
† 通讯作者 E-mail: moxp@mail.ioa.ac.cn