摘要
An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the ~esnel field integral for rectangular symmetric sources. From a known result that the circle or rectangle function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel Fourier transform. Two expansions are together inserted in this field integral, it is then expressible in terms of the simple algebraic functions. As examples, the numerical results for the sound pressure field are presented for the uniform rectangular piston transducer, in a good agreement with those directly evaluated from the Fresnel integral. A wide applicability of this approach is discussed in treatment of the ultrasonic field radiation problem for a large and important group of piston sources in acoustics.
An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the ~esnel field integral for rectangular symmetric sources. From a known result that the circle or rectangle function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel Fourier transform. Two expansions are together inserted in this field integral, it is then expressible in terms of the simple algebraic functions. As examples, the numerical results for the sound pressure field are presented for the uniform rectangular piston transducer, in a good agreement with those directly evaluated from the Fresnel integral. A wide applicability of this approach is discussed in treatment of the ultrasonic field radiation problem for a large and important group of piston sources in acoustics.
基金
Supported by the National Natural Science Foundation of China under Grant Nos 11074038 and 11374051
