Modal coupling in the vibration of fluid-loaded cylindrical shells

An approach is presented to evaluate the pressure field and vibratory response of a finite fluid-loaded cylindrical shell with infinite rigid extensions which are connected to the shell. The approach combines a generalized Fourier series or in vacuo eigenfunction expansion of the velocity field of the shell with a Green’s function and integral equation representation of the acoustic loading on the shell. Although modes with different circumferential wavenumbers are decoupled, all modes with identical circumferential wavenumbers are coupled via the fluid. The algebraic equations which account for this coupling include both shell impedances and acoustic impedances which are mode dependent. General integral expressions are presented for the acoustic impedances which include both self radiation and interaction impedances. In order to illustrate the general characteristics of these acoustic impedances, the impedances are investigated for a particular set of eigenfunctions. Low-frequency and asymptotic expressions are presented for both the self and interaction impedances. Extensive numerical results are also presented to illustrate general characteristics of the self and interaction impedances as a function of mode shape and frequency.