无障板圆形活塞换能器的辐射阻抗

Radiation impedance of the unbaffled circular piston transducer

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。

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.