The prediction of the elastic critical load of submerged elliptical cylindrical shell based on the vibro-acoustic model

• An approach predicting critical pressure of submerged elliptical shell is given.
• The natural frequencies of the system with different ellipticities are obtained.
• The critical pressure is obtained when natural frequency decreases to zero.
• The results show good agreement with published results.
• The presence of the ellipticity leads to lower elastic critical pressure.

Based on the vibro-acoustical model, an effective new approach to nondestructively predict the elastic critical hydrostatic pressure of a submerged elliptical cylindrical shell is presented in this paper. Based on the Goldenveizer–Novozhilov thin shell theory, the vibration equations considering hydrostatic pressures of outer fluid are written in the form of a matrix differential equation which is obtained by using the transfer matrix of the state vector of the shell. The fluid-loading term is represented as the form of Mathieu function. The data of the fundamental natural frequencies of the various elliptical cylindrical shells with different hydrostatic pressure and boundary conditions are obtained by solving the frequency equation using Lagrange interpolation method. The curve of the fundamental natural frequency squared versus hydrostatic pressure is drawn, which is approximately straight line. The elastic critical hydrostatic pressure is therefore obtained while the fundamental natural frequency is assumed to be zero according to the curve. The results obtained by the present approach show good agreement with published results.