Free vibration analysis of fluid-filled elliptical cylindrical shells

A method is presented for the free vibration analysis of finite fluid-filled elliptical cylindrical shells with variable curvature. Based on the Goldenveizer thin-shell theory, the vibration equations have been expressed as a matrix differential equation by using the transfer matrix and the fluid-loading term is represented as the form of Mathieu function, the transfer matrix is determined by use of the mid-Magnus series method. The natural frequencies are calculated numerically in terms of the matrix elements with a combination of appropriate initial guess and Lagrange interpolation method. The results of the degradation model obtained by the present method are compared to those of existing literatures. It is shown that the present method is highly accurate and the results are reliable. The sensitivity of the frequency parameter to the ellipticity parameter and the length of the shell are investigated respectively.