Axisymmetric Vibrations of a Vessel with Variable Thickness

Abstract

In this paper, the authors investigate the axisymmetric vibrations of a vessel with variable thickness composed of a cylindrical shell and two circular plates as its lids. They obtain the Lagrangian of the vessel expressed by quadratic forms of unknown boundary values and obtain the frequency equations from the minimum condition of the Lagrangian. Effects of the variations of thickness of circular plates and a cylindrical shell, of the length of a cylindrical shell etc.upon natural frequencies and mode shapes are clarified in discussions of numerical results.