球冠型换能器声辐射指向性分析

Analysis on acoustic directivity of spherical cap transducers

为了研究球冠型换能器的声辐射特性,在分离变量法求解球面坐标系下波动方程的基础上,采用基于球谐基傅里叶变换及边界条件的求解模型,给出了球冠型换能器声辐射的远场声压计算表达式和远场指向性表达式;仿真计算了球冠换能器的远场指向性随球冠极角、球半径及振动频率变化的特性,球冠所在球障板的直径和介质中声波的波长比决定着球冠声辐射指向性,在低频或波长大于球障板直径时,球冠声辐射呈无指向性,随着频率的增高即波长的减小或者球障板直径的增大,球冠声辐射的指向性越明显,波束开角越趋向于球冠的开角,而且波束开角内出现波浪状起伏越明显;试制了高频球冠型换能器基阵,测试了换能器基阵300 kHz的指向性,测试结果与理论计算相符合,验证了理论计算表达式的正确性,可为设计球冠型换能器及基阵提供理论指导。

In order to study acoustic radiation from the spherical cap transducer, a theoretical model was used by solving the wave equation in spherical coordinates using the method of separation of variables, based on the spherical harmonic Fourier transform and boundary condition. The calculation formulas for far field radiated pressure and directivity of spherical cap are derived. Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angle of spherical cap, radius of sphere baffle and operating frequency. Tile diameter of sphere baffle and wavelength in the media determine the directivity of acoustic radiation from a spherical cap. When the frequency is low or the wavelength is longer than the diameter of the sphere baffle, the acoustic radiation from a spherical cap is omnidirectional. With the increasing of the frequency or the diameter of the sphere baffle, the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle, furthermore the ripple in the beam is more obvious. Finally, the high frequency spherical cap transducer was fabricated and the directivity pattern were tested. As a result, the measurement data coincides with the theoretical calculation results and at the same time it verifies the correctness of theoretical formulas. This research can provide a guideline for designing the spherical cap transducers and arrays.