Free vibration analysis of infinitely long thick-walled hollow elliptical cylinder

Various shell theories have been used in the past to study the free vibration of the elliptic cylindrical shells. However, as the thickness ratio of the shell increases, the accuracy of the results for shear deformation theories declines. In this article, the classical theory of elasticity is employed to study the free vibration of a thick cylinder with an elliptic cross-section. The milestone of the analytically established model is based on Navier's equation, Helmholtz decomposition and Mathieu equations. The new model would specifically be applicable to the high thickness ratios where the structure response becomes highly complex and the high-order shell theories fail to obtain accurate results. Numerical example have been conducted in order to show the key effect of the cylinder's aspect ratio on the dispersion curve and deformed mode shape of the elliptical cylinder. Finally, the validity of the proposed analytical solution was compared to a finite element simulation in COMSOL MULTIPHYSICS.