Vibration modeling of variable thickness cylindrical shallow shells using extended Kantorovich method

Abstract

The current study aims to analytically model the vibration of variable thickness thin cylindrical shallow shells. First, Hamilton’s principle is used to derive the governing equations of motion of the system. The extended Kantorovich method (EKM) is then employed to study the corresponding eigenvalue problem. Using a single-term Galerkin approximation, the partial differential equations are converted to two sets of linear ordinary differential equations which are solved iteratively to find the system's natural frequencies and mode shapes. The findings of the study indicate that conducting only two iterations is sufficient to attain highly converged solutions. Studying the effect of element numbers on solution convergence shows that around ten elements provide a reasonable compromise between the solution accuracy and computational cost. The EKM results for thickness variations in either circumferential or axial directions are closely validated with FEA. Moreover, the EKM solutions match well with the results of other studies. In the end, by performing a parametric study, the effect of minimum to maximum thickness ratio on the first four natural frequencies of the shell is identified. The approach presented in this research can be employed as an efficient tool for fast and accurate design optimization of shallow shells.