Chen Duo, McGough Robert J
Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA.
J Acoust Soc Am. 2008 Sep;124(3):1526-37. doi: 10.1121/1.2950081.
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-Sommerfeld 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-Sommerfeld 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 II 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.
推导了用于快速计算变迹矩形活塞产生的时谐和瞬态近场压力的解析二维（2D）积分表达式。这些二维表达式是均匀激励活塞的快速近场方法（FNM）的扩展。将矩形活塞细分为较小的矩形后，使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，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。通过交换求和变量并进行分部积分，得到了二维变迹FNM表达式，所得表达式消除了变迹矩形活塞产生的压力场数值模型中原本存在的数值奇点。还描述了一种简化的时空分解方法，该方法进一步减少了瞬态压力场的计算时间。将结果与瑞利 - 索末菲积分以及边长等于四个波长的矩形源的FIELD II程序进行了比较。对于具有0.1归一化均方根误差（NRMSE）的时谐计算，变迹FNM比瑞利 - 索末菲积分快4.14倍，比FIELD II程序快59.43倍；对于0.01 NRMSE，变迹FNM比瑞利 - 索末菲积分快12.50倍，比FIELD II程序快155.06倍。对于具有0.1 NRMSE的瞬态计算，变迹FNM比瑞利 - 索末菲积分快2.31倍，比FIELD II程序快4.66倍；对于0.01 NRMSE，变迹FNM比瑞利 - 索末菲积分快11.90倍，比FIELD II程序快24.04倍。因此，二维变迹FNM非常适合在近场区域进行快速压力计算和精确的参考计算。
