An analytical formulation for the underwater acoustic radiation of a cylindrical shell with an internal flexural floor based on the reciprocity theorem

Abstract

Abstract An analytical formulation is proposed in this work to evaluate the underwater acoustic radiation of an infinite cylindrical shell containing an internal flexural floor, based on the reciprocity theorem which is applicable to linear acoustic-vibration coupling systems. The essence of this method is to convert the acoustic radiation problem into the problem of acoustic scattering through the reciprocity theorem. On this basis, the acoustic-vibration coupling problem of the three-dimensional shell-floor structure is reduced to an equivalent two-dimensional plane problem. Then, the acoustic-vibration coupling solution of the shell-floor structure can be obtained directly by using the analytical energy method. The correctness of the present calculation method and the correspondingly developed calculation codes is verified through comparisons in the following two aspects. First, the structural dry modes analytically derived using the present method are compared and agree well with those calculated by the finite element method (FEM). Second, the underwater acoustic radiation of an infinite cylindrical shell (not containing internal floor) is evaluated using the present reciprocity-based method and compared with the standard analytical solution derived using the conventional approach. It turns out that the results obtained via these two methods totally agree with each other. At last, the effect of three parameters (i.e. the thickness of the flexural floor, the radius of the cylindrical shell, and the structural loss factor) on the underwater acoustic radiation of the shell-floor structure is presented through several examples.