Cylindrical Shell Submerged in Bounded Acoustic Media: A Modal Approach

Abstract

The dynamics of a simply-supported cylindrical shell submerged in liquid hydrogen (LH 2 ) and liquid oxygen (LOX) are considered. The shell itself is bounded by a rigid outer cylinder with closed rigid ends. This conOguration gives rise to two ∞uid-Olled cavities{ an inner cylindrical cavity and an outer annular cavity. Such geometries are common in rocket engine design. This study computes the natural frequencies and modes of the ∞uid-structure system by combining the rigid wall acoustic cavity modes and the in vacuo structural modes into a system of coupled ordinary diAEerential equations. Eigenvalue veering is observed near the intersections of the curves representing natural frequencies of the rigid wall acoustic and the in vacuo structural modes. In the case of a shell submerged in LH 2 , system frequencies near these intersections are as much as 30% lower than the corresponding in vacuo structural frequencies. Due to its high density, the frequency reductions in the presence of LOX are even more dramatic. The forced response of the ∞uid-loaded shell subject to a harmonic point excitation is also presented. The forced response in the presence of ∞uid is diAEerent from the response of the structure in vacuo in a variety of ways. The frequency shifts that arise from consideration of the ∞uid alter the order of the resonant response peaks. In some cases, modes that are well separated in the in vacuo case are within close proximity in the ∞uid-loaded case (and vice-versa). The ∞uid-loaded structural responses also contain relatively small resonant peaks corresponding to system modes that are dominated by contributions from the ∞uid.