A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons
A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons
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DOI：
10.1121/1.2950081
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发表时间：
2008-09-01
影响因子：
2.4
通讯作者：
McGough, Robert J.
中科院分区：
文献类型：
--
作者：
Chen, Duo;McGough, Robert J.
推导了二维(2D)积分的解析表达式，用于快速计算变迹矩形活塞产生的时间谐和暂态近场压力。这些二维表达式是对均匀激励活塞的快速近场方法的推广。在将矩形活塞细分为更小的矩形后，利用矩形活塞的均匀激励FNM表达式计算每个较小矩形产生的压力，而变迹矩形活塞产生的总压力是所有细分矩形产生的压力的叠加。通过交换求和变量和进行分段积分，得到了二维变迹FNM表达式，消除了变迹矩形活塞压力场数值模型中存在的数值奇异性。文中还介绍了一种简化的时空分解方法，该方法进一步减少了瞬变压力场的计算时间。对四边等于四个波长的矩形声源，将计算结果与瑞利-索氏积分和FIELD II程序进行了比较。对于归一化均方根误差为0.1时的时间调和计算，变迹FNM比Rayleigh-Sotnmerfeld积分快4.14倍，是field II程序的59.43倍；对于0.01NRMSE，变迹FNM比Rayleigh-Sommerfeld积分快12.50倍，比field II程序快155.06倍。对于具有0.1 NRMSE的暂态计算，变迹FNM比Rayleigh-Sommerfeld积分快2.31倍，比field II程序快4.66倍；对于0.01 NRMSE，变迹FNM比Rayleigh-Sommerfeld积分快11.90倍，比field II程序快24.04倍。因此，二维变迹FNM非常适合于近场区域的快速压力计算和精确的参考计算。(C)2008年美国声学学会。
Analytical two-dimensional (2D) integral expressions are derived for fast calculations of time-harmonic and transient near-field pressures generated by apodized rectangular pistons. These 2D expressions represent an extension of the fast near-field method (FNM) for uniformly excited pistons. After subdividing the rectangular piston into smaller rectangles, the pressure produced by each of the smaller rectangles is calculated using the uniformly excited FNM expression for a rectangular piston, and the total pressure generated by an apodized rectangular piston is the superposition of the pressures produced by all of the subdivided rectangles. By exchanging summation variables and performing integration by parts, a 2D apodized FNM expression is obtained, and the resulting expression eliminates the numerical singularities that are otherwise present in numerical models of pressure fields generated by apodized rectangular pistons. A simplified time space decomposition method is also described, and this method further reduces the computation time for transient pressure fields. The results are compared with the Rayleigh-Sotnmerfeld integral and the FIELD II program for a rectangular source with each side equal to four wavelengths. For time-harmonic calculations with a 0.1 normalized root mean square error (NRMSE), the apodized FNM is 4.14 times faster than the Rayleigh-Sotnmerfeld integral and 59.43 times faster than the FIELD II program, and for a 0.01 NRMSE, the apodized FNM is 12.50 times faster than the Rayleigh-Sommerfeld integral and 155.06 times faster than the FIELD It program. For transient calculations with a 0.1 NRMSE, the apodized FNM is 2.31 times faster than the Rayleigh-Sommerfeld integral and 4.66 times faster than the FIELD II program, and for a 0.01 NRMSE, the apodized FNM is 11.90 times faster than the Rayleigh-Sommerfeld integral and 24.04 times faster than the FIELD II program. Thus, the 2D apodized FNM is ideal for fast pressure calculations and for accurate reference calculations in the near-field region. (C) 2008 Acoustical Society of America.