无障板圆形活塞换能器波束特性建模
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摘要
针对ka<π时无障板活塞声源波束特性不能用无限平面障板活塞换能器理论进行描述的问题,提出一种基于有限元方法结合曲线拟合的简便数学建模方法.模型采用了无限平面障板活塞换能器理论的基本函数表达,通过增加修正因子函数来改变模型的细节部分,用曲线拟合方法给出了较准确的两个修正因子函数的数学表达式。最终建立了无障板圆形活塞换能器波束特性经验公式模型,模型在ka为0.03～5.2范围内与有限元方法给出的波束曲线相一致,并且在ka取更大值时与无限平面障板活塞换能器理论公式等效.
The radiation theory of piston transducer in an infinite rigid plane baffle is not accurate to characterize the beam pattern of unbaffled circular piston transducer for ka<π.A simple mathematical modeling method based on the union of Finite Element Method(FEM)and curve fitting technique has been developed to solve this problem.Two modifying factors are introduced into the basic function expression of classical theory at first.Then the precise mathematical expressions of them are obtained through curve fitting method by numerical simulation.Thus the whole empirical formula model for beam pattern of unbaffled circular piston transducer is built.The results of this model agree well with the FEM solutions for ka in the range from 0.03 to 5.2.Furthermore,the model is identical with classical theory for greater ka.
The radiation theory of piston transducer in an infinite rigid plane baffle is not accurate to characterize the beam pattern of unbaffled circular piston transducer for ka<π.A simple mathematical modeling method based on the union of Finite Element Method(FEM)and curve fitting technique has been developed to solve this problem.Two modifying factors are introduced into the basic function expression of classical theory at first.Then the precise mathematical expressions of them are obtained through curve fitting method by numerical simulation.Thus the whole empirical formula model for beam pattern of unbaffled circular piston transducer is built.The results of this model agree well with the FEM solutions for ka in the range from 0.03 to 5.2.Furthermore,the model is identical with classical theory for greater ka.
引文
1 Sherman C H,Butler J L.Transducers and arrays for underwater sound(Second Edition).New York,2016:527—531
2杜功焕,朱哲民,龚秀芬.声学基础(第二版).南京,2001:344—351
3 Mellow T.On the sound field of a resilient disk in an infinite baffle.J.Acoust.Soc.Am.,2006; 120(1):90-101
4 Mellow T.On the sound field of a resilient disk in free space.J.Acoust.Soc.Am., 2008; 123(4):1880-1891
5 Lin Shuyu.Equivalent circuits and directivity patterns of air-coupled ultrasonic transducers.J.Acoust. Soc.Am.,2001; 109(3):949-957
6 Dekker D L,Piziali R L,Dong E.Effect of boundary conditions on the ultrasonic-beamcharacteristics of circular disks.J.Acoust.Soc.Am., 1974;56(1):87—93
7 Mast T D,Yu Feng.Simplified expansions for radiation from a baffled circular piston.J.Acoust.Soc.Am.,2005;118(6):3457-3464
8 He Xiping,Yan Xiuli,Li Na.Directivity pattern of the sound radiated from axisymmetric stepped plates.J.Acoust.Soc.Am.,2016; 140(2):1387-1396
9任惠娟,贺西平,扈凤.环状活塞声源辐射声场指向性研究.陕西师范大学学报(自然科学版),2007;35(3):40-43
10李锦,任中杰,林书玉.环状活塞换能器辐射声场研究.陕西师范大学学报(自然科学版),2003; 31(4):28-31
1 1李锦,林书玉.矩形活塞声源辐射声场研究.陕西师范大学学报(自然科学版),2003:31(1):39-42
12 Rajapan D.Performance of a low-frequency,multi-resonant broadband Tonpilz transducer.J.Acoust.Soc.Am.,2002;111(4):1692—1694
13秦雷,王丽坤,王钢等.具有大指向性开角及高发射电压响应的发射换能器.应用声学,2009; 26(6):472-475
14夏铁坚,郝浩琦,周利生等.大角度波束扫描的宽带平面阵研究.应用声学,2011; 30(1):13—18
15于祥龙,赵荣荣,唐少波.一种矩形辐射面宽波束换能器的设计.声学技术,2016;35(1):82-86
16唐少波,赵荣荣,田辉等.一种带障板宽波束宽带纵振动换能器.声学技术,2014; 33(2):184-188
17 Pillai S S,Ebenezer D D,Moosad K P B.Method to measure the efficiency and directivity index of underwater electroacoustic transducers.Proceedings of Sympol,2009:147-152
18莫喜平.无障板圆形活塞换能器的辐射阻抗.应用声学,2018;37(5):671-674
19莫喜平.ANSYS软件在模拟分析声学换能器中的应用.声学技术,2007;26(6):1279—1290
2杜功焕,朱哲民,龚秀芬.声学基础(第二版).南京,2001:344—351
3 Mellow T.On the sound field of a resilient disk in an infinite baffle.J.Acoust.Soc.Am.,2006; 120(1):90-101
4 Mellow T.On the sound field of a resilient disk in free space.J.Acoust.Soc.Am., 2008; 123(4):1880-1891
5 Lin Shuyu.Equivalent circuits and directivity patterns of air-coupled ultrasonic transducers.J.Acoust. Soc.Am.,2001; 109(3):949-957
6 Dekker D L,Piziali R L,Dong E.Effect of boundary conditions on the ultrasonic-beamcharacteristics of circular disks.J.Acoust.Soc.Am., 1974;56(1):87—93
7 Mast T D,Yu Feng.Simplified expansions for radiation from a baffled circular piston.J.Acoust.Soc.Am.,2005;118(6):3457-3464
8 He Xiping,Yan Xiuli,Li Na.Directivity pattern of the sound radiated from axisymmetric stepped plates.J.Acoust.Soc.Am.,2016; 140(2):1387-1396
9任惠娟,贺西平,扈凤.环状活塞声源辐射声场指向性研究.陕西师范大学学报(自然科学版),2007;35(3):40-43
10李锦,任中杰,林书玉.环状活塞换能器辐射声场研究.陕西师范大学学报(自然科学版),2003; 31(4):28-31
1 1李锦,林书玉.矩形活塞声源辐射声场研究.陕西师范大学学报(自然科学版),2003:31(1):39-42
12 Rajapan D.Performance of a low-frequency,multi-resonant broadband Tonpilz transducer.J.Acoust.Soc.Am.,2002;111(4):1692—1694
13秦雷,王丽坤,王钢等.具有大指向性开角及高发射电压响应的发射换能器.应用声学,2009; 26(6):472-475
14夏铁坚,郝浩琦,周利生等.大角度波束扫描的宽带平面阵研究.应用声学,2011; 30(1):13—18
15于祥龙,赵荣荣,唐少波.一种矩形辐射面宽波束换能器的设计.声学技术,2016;35(1):82-86
16唐少波,赵荣荣,田辉等.一种带障板宽波束宽带纵振动换能器.声学技术,2014; 33(2):184-188
17 Pillai S S,Ebenezer D D,Moosad K P B.Method to measure the efficiency and directivity index of underwater electroacoustic transducers.Proceedings of Sympol,2009:147-152
18莫喜平.无障板圆形活塞换能器的辐射阻抗.应用声学,2018;37(5):671-674
19莫喜平.ANSYS软件在模拟分析声学换能器中的应用.声学技术,2007;26(6):1279—1290