Response to 'Comment on `Modal analysis of a structure in a compressible fluid using a finite element/boundary element approach' ' [J. Acoust. Soc. Am. 102, 2445–2447 (1997)]

摘要

The authors thank Professors Pathak and Jalihal for their interest in our paper describing an iterative approach to estimating the in-water modal frequencies of a structure in a compressible fluid. Because of the requirement that the mode of interest remain uncoupled when the structure is submerged, the method is limited to nondimensional wave numbers, ka, of much less than one. In their Letter, Pathak and Jalihal showed that the method does not converge for some configurations of a piston in an infinite baffle, even though the in-water modal frequency is less than one. It is proposed that the lack of convergence is a result of the ideal nature of the piston problem. The particular configurations for which the method does not converge have one common characteristic. This is that the ka value corresponding to the in vacuo modal frequency is large, even though the final in-water ka is less than one. For these configurations, the radiation loading at the in vacuo frequency, which is the starting point for the iterative procedure, is dominated not by the radiation mass, but by the radiation damping. For realistic structures whose low-order modes remain uncoupled after submergence, the radiation mass is dominant at both the in vacuo and in-water modal frequencies. The proposed method is based on the assumption that this is the case, and was shown to be efficient and accurate for several modes of three multi-modal structures. Although it is believed that the piston variations presented by Pathak and Jalihal are outside of the realm of realistic structures, it will be shown that it is possible to achieve convergence to an accurate solution with a simple modification to the iterative procedure.