Page 135 - 《应用声学》2021年第2期

第 40 卷 第 2 期 Vol. 40, No. 2
2021 年 3 月 Journal of Applied Acoustics March, 2021

⋄ 研究报告 ⋄

短圆管换能器辐射阻抗

梁家宁 1,2,3† 莫喜平 1 柴 勇 1,3 刘永平 1,3

(1 中国科学院声学研究所 北京 100190)
(2 中国科学院大学 北京 100049)
(3 北京海洋声学装备工程技术研究中心 北京 100190)

摘要：辐射阻抗是换能器最重要的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。随着圆管换能器半径和高度的不断变化，想直接得到声场瑞利积分的解析解是十分困难的。该
文通过建立经验公式模型来解决此问题。首先，通过有限元软件计算圆管换能器辐射阻抗的数值解。然后利
用 MATLAB 工具进行曲线拟合。经过反复逼近拟合，建立圆管换能器辐射阻抗经验公式模型。与刚性扩展模
型计算出的傅里叶级数解相比，经验公式模型在 kr 值从 0.03 ∼ 10 范围内与有限元计算结果更为吻合，验证了
经验公式计算辐射阻抗的准确性。同时，在圆管更低高径比情况下，经验公式模型仍可较准确地计算辐射阻
抗。
关键词：辐射阻抗；圆管换能器；曲线拟合；数学表达式
中图法分类号: TB565+.1 文献标识码: A 文章编号: 1000-310X(2021)02-0303-05
DOI: 10.11684/j.issn.1000-310X.2021.02.019

Radiation impedance of short cylindrical transducer

LIANG Jianing 1,2,3 MO Xiping 1 CHAI Yong 1,3 LIU Yongping 1,3

(1 Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)
(2 University of Chinese Academy of Sciences, Beijing 100049, China)
(3 Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China)

Abstract: Radiation impedance is one of the most important radiated sound field characteristics of a trans-
ducer, which affects the resonance frequency, bandwidth, efficiency and radiated sound power of the transducer.
With the continuous change of the radius and height of a cylindrical transducer, it is very difficult to obtain
an analytical solution of the Rayleigh integral of sound field directly. An empirical formula model is built to
solve this problem. At first the numerical solutions of the radiation impedance of a cylindrical transducer are
calculated by the finite element software. Then curve fitting is done by the MATLAB tools. After a series of
attempts, the new empirical formula model could be established. Compared with the Fourier series solutions
calculated by the extended rigid model, the error of the empirical formula model could be decreased significantly
when kr is from 0.03 to 10. It is confirmed that this empirical formula model could calculate the radiation
impedance more accurately when the cylindrical transducer has a relatively small height-diameter ratio.
Keywords: Radiation impedance; Cylindrical transducer; Curve fitting; Mathematical expression

2020-05-14 收稿; 2020-07-15 定稿
作者简介: 梁家宁 (1995– ), 男, 山东济南人, 博士研究生, 研究方向: 声学换能器与功能材料。
† 通信作者 E-mail: liangjianing@mail.ioa.ac.cn