Free vibration of submerged finite elliptic cylindrical shell with ring stiffeners are examined with an analytical method. Stiffeners are averaged over the thin-walled isotropic elliptic cylindrical shell. The fluid sound pressure is described by the Helmholtz Equation. The ellipticity makes the difference between the symmetric and antisymmetric modal frequencies of the shell. The stiffeners have a greater influence on the vibration at relatively higher order circumferential modal parameters. The circumferential modal parameters corresponding to the fundamental frequency is affected by the ellipticity, shell length, stiffeners interval and depth.
The submerged circular cylindrical shell has been widely used in engineering for a long time. The study of submerged shell with ring stiffeners is of great significance due to the strengthening effect of the stiffeners. Paslay, Tatge, Wernick, Waksh and Muster (1969) gave an analytical procedure evaluated by experimental results for determining the natural frequencies for a submerged cylinder, and the beam theory was used to deduce the strain energy of the stiffeners which were assumed to be equally spaced. Chu, Pappa and Herman (1980) proposed a theoretical analysis for treating the free vibrations of submerged, ring-stiffened cylindrical shells with simply supported ends by utilizing the energy method and the effects of the stiffeners are averaged over the shell. Based on frequency characteristics (Plaut and Virgin, 1990; Souza and Assaid, 1991), the elastic critical pressure prediction of submerged ring-stiffened cylindrical shell is analyzed (Chen, Li, Zhu and Chen, 2014).
However, compared with the circular cylindrical shells, the elliptic cylindrical shells have their own advantage on capacity and equipment layout. And the studies on the vibration of elliptic cylindrical shell have received general attention. Elsbernd and Leissa (1973) presented the differential equations which govern the vibrations with initial stresses of thin non-circular cylinders in vacuum and results for the vibrations had been given for varying lengths, thicknesses and non-circularity. Irie, Yamada, and Notoya (1984) studied the natural frequencies for elliptical cylindrical shells in vacuum under six practical combinations of boundary conditions by using of the Ritz method. Ibrahim, Patel and Nath (2011) investigated the nonlinear periodic response characteristics of oval cylindrical shells by using of the finite strip method. The characteristics of fluid-elliptic cylindrical shell coupled system were also studied by scholars (Sarkar and Sonti, 2009). Hong and Kim (1995) gave analytical solutions for natural frequencies and mode shapes of elliptic cylindrical acoustic cavities. Willatzen and Voon (2006) studied flow-acoustic properties of elliptic-cylinder. Both references showed that when the ellipticity is small, natural frequencies of elliptic cylindrical acoustic cavities are similar to those of circular cylindrical acoustic cavities. Recently, Li, Xiong, Zhu and Xiong (2014) presented a new approach to nondestructively predict the elastic critical hydrostatic pressure of a submerged elliptical cylindrical shell by using transfer matrix method. Zhang, Li, Zhu, Yang and Miao (2017) studied the free and forced vibration of a submerged elliptical cylindrical shell and the main parameters such as ellipticity parameter, shell thickness ratio and so on were discussed in detail.