Natural frequency split estimation for inextensional vibration of imperfect hemispherical shell

In this study, mathematical model of hemispherical shell is introduced using inextensional vibration mode shapes. Adopting energy equations, the natural frequency of the shell is determined by applying Rayleighʹs energy method. Further, the vibration for imperfect shell is investigated with point mass elements representing imperfections on the structures. Also, the effects are considered via energy relations, and the split amount of the natural frequencies can be determined. Finally, the influences of point mass are presented by explicit functions for the split of the natural frequency and shifting angle of mode orientation. Based on the proposed model of imperfect shell with multiple point masses, the structure can be expressed as an equivalent single mass model.