高斯束展开法的注记之二：简单支撑矩形换能器声场

进一步给出高斯束展开法的推广。将文献中的圆形函数的高斯函数展开作为已知的结果,通过傅里叶或贝塞尔变换,余弦函数也可表示成高斯函数的叠加。因而菲涅尔场积分可以简化成一系列简单的代数函数的求和。利用这一方法,计算了简单支撑矩形活塞换能器声场分布。与解析解的数值结果相比,结果相当一致。

Further Notes on the Gaussian Beam Expansion:Ⅱ. Sound Fields from the Simply-Supported Rectangular Transducer

Abstract: A further extension to the Gaussian-beam expansion is alternatively presented. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Fourier or Bessel transform. Accordingly, the Fresnel field integral is then expressible in terms of the simple algebraic functions. As examples, the numerical results are given for the sound pressure field radiated from the rectangular piston transducer simply supported at its edges, in a good agreement with those from an analytic solution expressed by complex Fresnel functions.