Analysis of the energy transmission in compound cylindrical shells with and without internal heavy fluid loading by boundary integral equations and by Floquet theory

This paper addresses three aspects of the steady-state free vibration of non-uniform (i.e., composed of alternating elements) elastic cylindrical shells with and without internal heavy fluid loading, which have not previously been studied in detailed form. Firstly, Floquet theory is applied to detect the location of frequency band gaps in an infinitely long periodic fluid-filled cylindrical shell vibrating in the ‘beam-type’ mode m = 1 and in the ovalling mode m = 2 in the framework of two simplified theories. As a prerequisite for this study, the validity range of these theories is estimated by comparison of the resulting dispersion curves with the exact solution. Secondly, the boundary equations are derived for a cylindrical shell with internal heavy fluid loading in the framework of the suggested theories. The methodology of boundary integral equations is used to obtain exact solutions for the problems of free vibrations of a finite shell and wave propagation in an infinitely long shell. Finally, the energy transmission in a semi-infinite non-uniform cylindrical shell with and without internal heavy fluid loading is addressed; predictions obtained by use of Floquet theory are compared with the exact solution obtained by the method of boundary integral equations.