Free vibration of truncated conical shells with elastic boundary constraints and added mass

Abstract

Most of the research on truncated conical shells focuses on the dynamics with classical boundary conditions. However, less attention has been given to the non-classical boundary conditions due to the lack of a unified displacement function, such as a boundary with point constraint or partial constraint, or a boundary with added mass, which exists in engineering practice. In this study, we investigate the free vibration of the truncated conical shell with arbitrary boundary conditions, including elastic and inertia force constraints. The equations of motion with elastic boundary constraints are formulated by employing Hamilton's principle and the thin-walled shallow shell theory of the Donnell type. The solutions of the shells are obtained using Fourier series in circumferential directions and power series in meridional directions, with various boundary conditions achieved through the choice of stiffness, which is a unified solution procedure. The procedure proposed was validated by comparing the results obtained with results available in the literature on classical boundary conditions and with the finite element method results for the non-classical boundary conditions. Numerical simulations were carried out to illustrate the sensitivity of the shell frequency to the stiffness parameters and the moment of inertia effect on frequency, and to present the circumferential modal jumping phenomena with patterns.