Theory and numerical simulation for a cylindrical array by broadband constant beam pattern approach

A broadband constant beam pattern (CBP) array is an acoustic array whose beam patterns are independent of operating frequencies. In this article, the theoretical far-field acoustic beam pattern analytic formulations have been mathematically derived for a cylindrical array on an infinite rigid cylinder, after applying the Fourier series expansion, the Fourier sine or cosine transform, and the stationary phase method to the Helmholtz equation with boundary conditions. When the ratio of the array radius over the operating frequency wavelength was large, the horizontal (xoy) plane beam patterns demonstrated broadband CBP performances under the far-field conditions. The vertical (xoz) plane acoustic beam patterns are determined by the array vertical aperture shading's Fourier spectrum coupled with the residuals from the asymptotic approximations of the Hankel function and its derivative. The theoretical results matched with the results by Kirchhoff's integral numerical simulation with various horizontal shading examples for directional acoustic beams by the broadband CBP approach.